An particle in a 1-D box of length L =2A? has allowed energy levels that include

Question

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.

An particle in a 1-D box of length L = 2A unknown. has allowed energy levels that include 84.82 eV and 150.79 eV, however, the quantum numbers for these two states are Part A - What is the ground-state energy of the system? 0 Ei = 21.2 eV OE1 37.7eV 0 E1 = 16.75 eV 0 E1=28.3eV ( E, = 9.42eV 0 E, = 5.30 eV Submit My Answers Give Up Part B - What is the de Broglie wavelength for the n 2 state? O 1.0 A O 2.0 A 3.0 A O 2.5A 2.5A O 1.5A 0.5A Submit My Answers Give Up

Explanation / Answer

En = (n^2 *h^2)/(8 mL^2)

84.82 = (n1^2 * (6.62*10^-34)^2)/(8*mL^2)
(8*mL^2)/( 6.62*10^-34)^2 = n1^2/84.82

150.79 = ((n2^2 * (6.62*10^-34)^2)/(8*mL^2))
(8*mL^2)/( 6.62*10^-34)^2 =  n2^2/150.79

n1^2/84.82 = n2^2/150.79
n1/n2 = sqrt(84.82/150.79)
n1/n2 = 3/4

(8*m (2*10^-10)^2)/( 6.62*10^-34)^2 = 3^2/(84.82 *1.6*10^-19)
m = 9.08 *10^-31 Kg

E1 = n^2 * h^2 / 8 * m*L^2
E1 = 1 * ( 6.62*10^-34)^2 / ((8*9.08 *10^-31 (2*10^-10)^2))]/(1.6*10^-19) eV
E1 = 9.42 eV


= h/sqrt(2*m*E2)
E2 = (2^2 * ( 6.62*10^-34)^2) / ((8*9.08 *10^-31 (2*10^-10)^2))

= (6.63*10^-34) / sqrt(2*9.08*10^-31 *6.03*10^-18)
= 2.0 * 10^-10 m
= 2.0 A

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