If the radius of the electron orbit in the n = 1 level of the hydrogen atoms is 0.0529 nm,what is its radius for the n = 4 level? (Assume the Bohr model is valid).
A) 1.32 nm
B) 0.265 nm
C) 0.106 nm
D) 0.846 nm

Question

Quizplus · Accepted Answer

The radius of electron in the nth level of hydrogen atom can be calculated using the following formula:

r = (n²h²ε₀)/(πme²)

where 
r = radius of orbit
n = principal quantum number
h = Planck's constant
ε₀ = permittivity of free space
me = mass of electron
e = elementary charge

For n = 1, r = 0.0529 nm

For n = 4, we need to calculate the radius using the above formula:

r = (4²h²ε₀)/(πme²) = (16h²ε₀)/(πme²)

Substituting the values of h, ε₀, and me, we get:

r = (16 x 6.626 x 10^-34 J s x (8.854 x 10^-12 F/m) ) / (π x (9.109 x 10^-31 kg) x (1.602 x 10^-19 C)^2)

r = 8.46 x 10^-11 m = 0.846 nm

Therefore, the radius of electron orbit in the n = 4 level of hydrogen atom is 0.846 nm, which is closest to option D (0.846 nm).

If the Radius of the Electron Orbit in the N