Question

Item 5

An particle in a 1-D box of length L=2A∘ has allowed energy levels that include 84.82 eV and 150.79 eV; however, the quantum numbers for these two states are unknown.

Part A - What is the ground-state energy of the system?

E1=9.42eV

E1=37.7eV

E1=5.30 eV

E1=16.75 eV

E1=28.3eV

E1=21.2 eV

Part B - What is the de Broglie wavelength for the n=2 state?

2.5A∘

0.5A∘

1.5A∘

3.0 A∘

1.0 A∘

2.0 A∘

Answer 1

part A:

as energy levels are quantized, ground energy level will be the highest common factor of all energy levels

hence taking HCF of 84.82 and 150.79 eV, we get ground state energy level to be 9.42 eV

(easy menthod to do so is to divide 84.82 eV by integers 1,2,3,4 etc and see for which value , 150.79 is also an integral multiple )

part b:

for n th state, de broglie wavelength is given by 2*L/n

here L=2 Angstrom

n=2
hence wavelength=2*2/2=2 Angstrom

hence 2 A is correct answer.