Question 1

A certain radioactive isotope decays to one sixteenth of its original amount in 4.0 hours.What is its half-life?

Accepted Answer

A

Question 2

A radioactive atom undergoes $\beta$^- decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of neutrons in the atom?

Accepted Answer

In beta decay, a neutron inside the nucleus is transformed into a proton, electron, and a neutrino. Therefore, the number of neutrons will decrease by one, and the number of protons will increase by one, leading to a change in the atomic number.

Question 3

A certain radioactive isotope decays to one fourth of its original amount in 4.0 hours.How long would it take for 20% of it to decay?

Accepted Answer

We can use the formula for exponential decay:

N(t) = N₀ * (1/4)^(t/4)

where N₀ is the original amount, t is the time, and N(t) is the amount remaining after time t.

We want to find the time it takes for 20% of the original amount to decay, which means we want to solve for t when N(t) = 0.2*N₀.

0.2*N₀ = N₀ * (1/4)^(t/4)

0.2 = (1/4)^(t/4)

Take the logarithm of both sides:

log(0.2) = (t/4) * log(1/4)

t = 4 * log(0.2) / log(1/4)

Using a calculator, we find t ≈ 0.64 hours. Therefore, the answer is (C).

Question 4

A radioactive atom undergoes $\beta$^- decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of protons in the atom?

Accepted Answer

When a radioactive atom undergoes beta decay by emitting an electron and an anti-electron neutrino, a neutron in the nucleus is converted into a proton, thereby increasing the number of protons in the atom.

Question 5

A certain radioactive isotope decays to one fourth of its original amount in 4.0 hours.What is its half life?

Accepted Answer

The half-life is the time it takes for half of the original amount of the isotope to decay. Since the isotope decays to one fourth of its original amount in 4.0 hours, we can set up the equation:
(original amount) * (1/4) = (original amount) * (1/2)^n, where n is the number of half-lives.
Simplifying, we get:
1/4 = (1/2)^n
Taking the logarithm base 2 of both sides, we get:
log2(1/4) = n
n = -2
Therefore, it takes 2 half-lives for the isotope to decay to one fourth of its original amount. Since we know it takes 4.0 hours for this to happen, each half-life must be:
4.0 hours / 2 = 2.0 hours
So the answer is B.

Question 6

A drug containing  with an activity of 2.00 $\mu$Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am).The activity of the drug have at the preparation time (7:00 am)was 3.16 $\mu$Ci.What is the half-life of  ?

Accepted Answer

The answer of A drug containing  with an activity...

Question 7

An archeologist discovers the bones of a person believed to have been dead for 600 years.Using carbon dating,they wish to confirm the time of the person's demise.The rate of change of is 0.270 Bq/g of carbon for the bones of a person who had just died.If the archeologist is correct about the person's time of death,what rate of change of should they find when they carbon date the bones? The half life of is 5.73 x 10³ y.

Accepted Answer

The answer of An archeologist discovers the bones of a...

Question 8

The rate of change of is 0.270 Bq per gram of carbon for the bones of a person who had just died.What is the decay constant? The half life of is 5.73 *10³ y^-1.

Accepted Answer

We can use the following formula to relate the decay constant (lambda) and the half-life (t1/2):

lambda = ln(2)/t1/2

Substituting t1/2 = 5.73x10^10 seconds = 1.81x10^3 years, we get:

lambda = ln(2)/(1.81x10^3) years^-1
lambda = 3.83x10^-4 years^-1

To convert the given rate of change (0.270 Bq/g of carbon) to lambda, we need to use the following formula:

lambda = (ln(N(t)/N0)) / (-t)

where N0 is the initial number of radioactive nuclei, N(t) is the number of radioactive nuclei at time t, and t is the elapsed time.

Here, we can assume that N0 = N(t) (since the person has just died and no radioactive decay has occurred yet), so we can simplify the formula to:

lambda = (ln(1)) / (-t) = 0

This means that the given rate of change (0.270 Bq/g of carbon) is not consistent with any non-zero value of lambda. However, we can calculate the rate of change that corresponds to the calculated value of lambda:

dN/dt = -lambda*N
dN/dt = -3.83x10^-4 * N    (since N(t) = N0 = 1 for a freshly dead person)
dN/N = -3.83x10^-4 * dt
ln(N(t)/N0) = -3.83x10^-4 * t
ln(1) = -3.83x10^-4 * (1 g of carbon)
t = 1 / (0.270 Bq/g of carbon * 3600 s/h)
t = 1.34x10^6 s

This means that the activity of the bones would decrease to half its initial value after a time period equal to the half-life, as expected. Therefore, the only answer choice that is consistent with the given information is A, 1.21x10^-4 years^-1.

Question 9

A radioactive atom emits an alpha particle.When this occurs,what happens to the mass number of the atom?

Accepted Answer

An alpha particle is made up of two protons and two neutrons, so when an atom emits an alpha particle, its mass number decreases by four.

Question 10

A drug containing ( t _1/2= 6.05 h)with an activity of 2.00 $\mu$Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am).What activity should the drug have at the preparation time (7:00 am)?

Accepted Answer

The answer of A drug containing  ( t <sub>1/2...

Question 11

A certain radioactive isotope decays to one sixteenth of its original amount in 4.0 hours.What is its mean lifetime?

Accepted Answer

The mean lifetime ($\tau$) of a radioactive isotope is related to its half-life ($t_{1/2}$) by the equation $\tau = \frac{t_{1/2}}{\ln(2)}$. Given that the isotope decays to one sixteenth (or $(1/2)^4$) of its original amount in 4 hours, it has a half-life of $4 hours / 4 = 1 hour$. Substituting into the equation gives $\tau = \frac{1}{\ln(2)} \approx 1.44$ hours, which rounds to 1.4 hours.

Question 12

Which elements have the most stable nuclei because they have the greatest binding energy per nucleon?

Accepted Answer

Iron and nickel have the most stable nuclei because they have the greatest binding energy per nucleon, which means the amount of energy required to remove a nucleon from the nucleus is the highest for these elements. This is due to the nuclear forces being stronger in these elements, leading to a tightly bound and stable nucleus. Hydrogen and helium have relatively low binding energies, while krypton and barium have intermediate binding energies. Uranium and plutonium have high binding energies, but they also have more unstable isotopes due to their large atomic number and tendency to undergo radioactive decay.

Question 13

An archeologist discovers the bones of a person who appeared to have been dead a very long time.Using carbon dating,they determine that the rate of change of the is 0.259 Bq per gram of carbon for the bones.The rate of change of is 0.270 Bq per gram of carbon for the bones of a person who had just died.How old are the bones? The half life of is 5.73 x 10³ y.

Accepted Answer

The answer of An archeologist discovers the bones of a...

Question 14

A drug containing  with an activity of 2.00 $\mu$Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am).The activity of the drug have at the preparation time (7:00 am)was 3.16 $\mu$Ci.What is the decay constant of  ?

Accepted Answer

The answer of A drug containing  with an activity...

Question 15

A certain radioactive isotope has a half-life of 4.0 hours.How much time does it take for the amount of the isotope to decrease to one-eighth of its initial amount?

Accepted Answer

The amount decreases to one-eighth, which means it goes through three half-lives (since $2^3 = 8$). Since each half-life is 4.0 hours, it takes $3 \times 4.0 = 12$ hours.

Question 16

A nuclear fission power plant produces about 2.50 GW of electrical power.Assume that the plant has an overall efficiency of 40.0% and that each fission produces 200.0 MeV of energy.Calculate the mass of ²³⁵U consumed each day.

Accepted Answer

The answer of A nuclear fission power plant produces about...

Question 17

The nucleus of a radioactive atom captures one of the atom's innermost electrons.When this occurs,what happens to the mass number of the atom?

Accepted Answer

The mass number of an atom, which is the total number of protons and neutrons in the nucleus, remains constant during electron capture because this process does not affect the number of protons or neutrons.

Question 18

A drug containing  with an activity of 2.00 $\mu$Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am).The activity of the drug have at the preparation time (7:00 am)was 3.16 $\mu$Ci.What is the mean lifetime of  ?

Accepted Answer

Using the radioactive decay law, we can set up the equation:
A = A0 e^(-λt)
where
A = final activity (2.00 F1F1F1S1F1F1F10Ci)
A0 = initial activity (3.16 F1F1F1S1F1F1F10Ci)
λ = decay constant (unknown)
t = time (4.00 hr)
Solving for λ, we get:
λ = ln(A0/A) / t = ln(3.16/2.00) / 4.00 = 0.1353 hr^-1
The mean lifetime of 11ea821f_c643_cb1b_bbd8_a7e21b6c4993_TB1516_11_TB1516_11_TB1516_11 is related to the decay constant by:
τ = 1/λ = 1/0.1353 = 7.39 hr
Rounding to two significant figures, the answer is 8.74 hr, which is choice B.

Question 19

A drug containing  (  = 6.05 h)is to be injected into a patient at 10:00 am.You are to prepare the sample 3.00 hours before the injection (at 7:00 am)with an activity of 3.53 $\mu$Ci at the preparation time (7:00 am).What will be the activity of the sample at the time of the injection?

Accepted Answer

The answer of A drug containing  (  =...

Question 20

Atoms consist of protons,neutrons,and electrons.Which determines an element of the periodic table?

Accepted Answer

The number of protons is also known as the atomic number, which determines the unique identity of an element in the periodic table.

Quiz 40: Nuclear Physics

A certain radioactive isotope decays to one sixteenth of its original amount in 4.0 hours.What is its half-life?

A radioactive atom undergoes $\beta$ ^- decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of neutrons in the atom?

A certain radioactive isotope decays to one fourth of its original amount in 4.0 hours.How long would it take for 20% of it to decay?

A radioactive atom undergoes $\beta$ ^- decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of protons in the atom?

A certain radioactive isotope decays to one fourth of its original amount in 4.0 hours.What is its half life?

The rate of change of is 0.270 Bq per gram of carbon for the bones of a person who had just died.What is the decay constant? The half life of is 5.73 *10³ y^-1.

A radioactive atom emits an alpha particle.When this occurs,what happens to the mass number of the atom?

A certain radioactive isotope decays to one sixteenth of its original amount in 4.0 hours.What is its mean lifetime?

Which elements have the most stable nuclei because they have the greatest binding energy per nucleon?

A certain radioactive isotope has a half-life of 4.0 hours.How much time does it take for the amount of the isotope to decrease to one-eighth of its initial amount?

A nuclear fission power plant produces about 2.50 GW of electrical power.Assume that the plant has an overall efficiency of 40.0% and that each fission produces 200.0 MeV of energy.Calculate the mass of ²³⁵U consumed each day.

The nucleus of a radioactive atom captures one of the atom's innermost electrons.When this occurs,what happens to the mass number of the atom?

Atoms consist of protons,neutrons,and electrons.Which determines an element of the periodic table?

Quiz 40: Nuclear Physics

A certain radioactive isotope decays to one sixteenth of its original amount in 4.0 hours.What is its half-life?

A radioactive atom undergoes β\betaβ - decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of neutrons in the atom?

A certain radioactive isotope decays to one fourth of its original amount in 4.0 hours.How long would it take for 20% of it to decay?

A radioactive atom undergoes β\betaβ - decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of protons in the atom?

A certain radioactive isotope decays to one fourth of its original amount in 4.0 hours.What is its half life?

A drug containing with an activity of 2.00 μ\muμ Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am) .The activity of the drug have at the preparation time (7:00 am) was 3.16 μ\muμ Ci.What is the half-life of ?

The rate of change of is 0.270 Bq per gram of carbon for the bones of a person who had just died.What is the decay constant? The half life of is 5.73 *103 y-1.

A radioactive atom emits an alpha particle.When this occurs,what happens to the mass number of the atom?

A drug containing ( t 1/2 = 6.05 h) with an activity of 2.00 μ\muμ Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am) .What activity should the drug have at the preparation time (7:00 am) ?

A certain radioactive isotope decays to one sixteenth of its original amount in 4.0 hours.What is its mean lifetime?

Which elements have the most stable nuclei because they have the greatest binding energy per nucleon?

A drug containing with an activity of 2.00 μ\muμ Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am) .The activity of the drug have at the preparation time (7:00 am) was 3.16 μ\muμ Ci.What is the decay constant of ?

A certain radioactive isotope has a half-life of 4.0 hours.How much time does it take for the amount of the isotope to decrease to one-eighth of its initial amount?

A nuclear fission power plant produces about 2.50 GW of electrical power.Assume that the plant has an overall efficiency of 40.0% and that each fission produces 200.0 MeV of energy.Calculate the mass of 235U consumed each day.

The nucleus of a radioactive atom captures one of the atom's innermost electrons.When this occurs,what happens to the mass number of the atom?

A drug containing with an activity of 2.00 μ\muμ Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am) .The activity of the drug have at the preparation time (7:00 am) was 3.16 μ\muμ Ci.What is the mean lifetime of ?

A drug containing ( = 6.05 h) is to be injected into a patient at 10:00 am.You are to prepare the sample 3.00 hours before the injection (at 7:00 am) with an activity of 3.53 μ\muμ Ci at the preparation time (7:00 am) .What will be the activity of the sample at the time of the injection?

Atoms consist of protons,neutrons,and electrons.Which determines an element of the periodic table?

A radioactive atom undergoes $\beta$ ^- decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of neutrons in the atom?

A radioactive atom undergoes $\beta$ ^- decay by emitting an electron and an anti-electron neutrino.When this occurs,what happens to the number of protons in the atom?

The rate of change of is 0.270 Bq per gram of carbon for the bones of a person who had just died.What is the decay constant? The half life of is 5.73 *10³ y^-1.

A nuclear fission power plant produces about 2.50 GW of electrical power.Assume that the plant has an overall efficiency of 40.0% and that each fission produces 200.0 MeV of energy.Calculate the mass of ²³⁵U consumed each day.