Problem 1.18 Part A Determine the momentum for the n = 2 state of the Bohr model

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Problem 1.18

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.

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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.

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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.

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.

dB = 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.

E = Eh K = Eh

Explanation / Answer

A) Momentum,p = n*h/(2*pi*rn) ; where h = Planck's constant ; rn = 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

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