1. Consider an neon atom confined to a one-dimensional box of length 1.50 angstr
ID: 716718 • Letter: 1
Question
1. Consider an neon atom confined to a one-dimensional box of length 1.50 angstroms. What is the energy difference for this atom, in Joules, between the n=9 and n=8 energy levels? Include units in your answer, and use X.XXeXX for the answer format.
2. Now consider the same atom confined to the one-dimensional box of length 4.60 angstroms. What is the energy difference for this atom, in Joules, between the n=9 and n=8 energy levels? Include units in your answer, and use X.XXeXX for the answer format.
3. Consider a particle confined to a line of length L. As the particle mass increases, the energy gap between adjacent energy levels:
A. decreases.
B. increases
4. Consider a particle confined to a line of length L. As the length of the line increases, the energy gap between adjacent energy levels:
A. stays constant.
B. decreases.
I need help with this problem 4 Parts. Please show all work! Thank you!
Explanation / Answer
According to the energy expression for the particle in a one-dimensional box En=(n2h2/8mL2)
where n=1,2,3,....., h is the Planck's constant whose value is 6.63*10-34 Jaule. sec, m is the mass of the particle and L is the length of the box.
1. The energy difference between n=9 and n= 8 is (nf2-ni2)h2/8mL2 = (92-82)*(6.63*10-34 Jaule. sec)/(8*mass of neon atom in kg*(1.5*10-10)2) Jaule
mass of neon atom= 20 amu= 20 *1.6*10-27 kg and length (L) of the box is 1.5*10-10 meter
2. Put the value of L as 4.6*10-10 meter. Other things will be the same as above. Units will be in Jaule.
3. As the particle mass increases the energy gap between adjacent energy levels decreases as the energy gap is inversely proportional to the mass of the particle.
4. As the length of the line increases, the energy gap between adjacent energy levels decreases.
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