According to the Bohr model of a hydrogen atom, the frequency of light radiated

Question

According to the Bohr model of a hydrogen atom, the frequency of light radiated by an electron moving from an orbit n_1 to an orbit n_2 corresponds to the energy level difference between n_1and n_2 of where and where m_e is the electron mass, Z is the atomic number, e is the magnitude of the electron charge, epsilon_0 is the permittivity of free space, and h is Planck's constant divided by 2 pi. In the case of hydrogen (Z = 1) E_0 = -13.6 eV. Find the frequency of light f radiated by an electron moving from orbit n_1 = 2 to n_2 = 1 inside of a He^+ ion. Express your answer in hertz to three significant figures. In the Bohr model of hydrogen, the radius of the n^th orbit is defined as where is called the Bohr radius. Find the radius r_1 of a valence orbital for a He^+ ion. Express your answer in meters to three significant figures.

Explanation / Answer

A)
Eo = -13.6* Z^2
= -13.6*2^2
= -13.6*4
= - 54.4 eV
= -54.4*1.6*10^-19 J
= -8.704*10^-18 J
E = Eo* (1/n1^2 - 1/n2^2)
= -8.704*10^-18 * (1/2^2 - 1)
= -8.704*10^-18 * (1/2^2 - 1)
= 6.528*10^-18 J
use:
f = E/h
= (6.528*10^-18) / (6.626*10^-34)
= 9.85*10^15 Hz
Answer: 9.85*10^15 Hz

B)
ao = 5.29*10^-11 m
rn = ao*n^2/Z
= (5.29*10^-11)* 1^2 / 2
= 2.645*10^-11 m
Answer: 2.645*10^-11 m

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