Question

Chose the right answer

a) If we decrease the size of a quantum dot that contains an electron, what happens to the energy levels?

1-Decrease

2-remain the same

3-increase

b) If two quantum states are degenerate, which is true?

1- They have identical momenta.

2- They have identical wave functions

3- They have identical energies

C) Which is true about the electron in a hydrogen atom?

1-Its total energy and potential energy are negative

2-Its kinetic energy and potential energy are negative

3-Its total energy and kinetic energy are negative.

d) Which quantum number determines the energy of the hydrogen atom?

1- orbital quantum number

2- principal quantum number

3- orbital magnetic quantum number

Answer 1

1. If we decrease the size of quantam dot which contain electron, the energy levels increases.

2.two quantum states are degenerate if they have the same energy. The fact that the two quantum states are different implies that they are orthogonal to each other. So I would state the two conditions E 1 = E 2 E1=E2 and 〈 ψ 1 | ψ 2 〉 = 0 〈ψ1|ψ2〉=0 as the condition for degeneracy. Clearly the two eigenstates n,-n in your example are orthogonal to each other.

3.The electron (positive) is attracted to the nucleus (negative). So to remove it from the atom (as per the above statement) we must supply energy, so PE is negative. (KE was positive because it is simply energy that the electron has due to its motion.so actually, Total energy and potential energy is negative as we need energy to push electron moves out of tht orbit.

4.Quantum number is the principal quantum number (n) which describes the main energy level and size of an orbital is responsible for hydrogen atom.