Question

Problem 1.18

Values for some properties of the n = 1 state of the Bohr model of the hydrogen atom are given in the following table. Write the value of the same parameter (in the same units) for the n = 2 state.

parameter	n = 1	n = 2
momentum (kgms)	1.99 ⋅ 10-24
de Broglie wavelength (nm)	0.333
kinetic energy (Eh)	0.500
transition energy to n = 3 (Eh)	0.444

Part A

Determine the momentum for the n = 2 state of the Bohr model of the hydrogen atom.

Express your answer using three significant figures.

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Part B

Determine de Broglie wavelength for the n = 2 state of the Bohr model of the hydrogen atom.

Express your answer using three significant figures.

p =

kgms

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Part C

Determine the kinetic energy for the n = 2 state of the Bohr model of the hydrogen atom.

Express your answer using three significant figures.

λdB =

nm

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Part D

Determine the transition energy from n = 2 to n = 3 for the Bohr model of the hydrogen atom.

Express your answer using three significant figures.

ΔE =

Eh

K =

Eh

Answer 1

A) Momentum,p = n*h/(2*pi*r_n) ; where h = Planck's constant ; r_n = radius of the shell = 0.53*n² A⁰

Thus, for n = 2, momentum = (2*6.63*10^-34)/(2*3.14*0.53*10^-10*4) = 9.96*10^-25 kgm-s

B) de Broglies wavelength = h/p = (6.63*10^-34)/(9.96*10^-25) = 6.657*10^-10 m = 0.666 nm

C) K.E = (1/2)*p²/m = (1/2)*(9.96*10^-25)/9.1*10^-31 = 5.45*10^-19 J

D) Energy = -13.6/n² eV

Thus, for n = 2 , E₂ = -3.4 eV

for n = 3 , E₃ = -1.51 eV

Thus, transition energy = -1.51- (-3.4) = 1.89 eV = 3.024*10^-19 J