A line from the Pfund series has the frequency 8.02 * 10¹³ Hz. What value of n₂ generates this line in the spectrum?

Question

Quizplus · Accepted Answer

The formula for the Pfund series is given by 1/λ = RZ^2(1/n1^2 - 1/n2^2), where R is the Rydberg constant, Z is the atomic number, and n1 and n2 are integers representing the energy levels involved in the transition. Rearranging the formula gives n2 = n1/ (1 - λ/RZ^2n1^2).

For the given frequency, we can use the formula ν=c/λ to obtain the wavelength λ = c/ν = 3x10^8 m/s / 8.02x10^15 Hz = 3.74x10^-8 m. From this wavelength, we can find the energy of the photon using E = hc/λ, where h is Planck's constant and c is the speed of light. This gives E = 5.28x10^-18 J.

We can then use the energy formula for hydrogen, E = -13.6 eV * Z^2 / n^2, to find the value of n. Rearranging the formula gives n = sqrt(-13.6 eV * Z^2 / E). Substituting in the values, we get n = 8.

Therefore, the correct answer is D) 8.

A Line from the Pfund Series Has the Frequency 8