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_1 and n_2 of E = E_0 (1/n^2_1 - 1/n^2_2), where E_0 = m_e Z^2 e^4/32 pi^2 elementof^2_0 h^2, and where m_e is the electron mass, Z is the atomic number, e is the magnitude of the electron charge, elementof_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. f = 32894736.84 Hz In the Bohr model of hydrogen, the radius of the n^th orbit is defined as r_n = a_0 n^2/Z, where a_0 = 4 pi elementof h^2/m_e e^2 = 5.29 times 10^-11 m 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. r_1 = 2.65 times 10^-11 m

Explanation / Answer

now we find the frequency of electron travel from n1=2 to n2=1

basing on the concept of bohr atomic model

hf=12.8*10^-18Z^2{1/n1^2-1/n2^2}

6.63*10^-34*f=12.8*10^-18*2^2{1/2^2-1/1^2}

frequency f=153.6*10^-18/26.52*10^-34

=5.8*10^16 Hz

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