Question

1. As we increase the quantum number of an electron in a one-dimensional, infinite potential well, what happens to the number of maximum points in the probability density function?

It increases.

It decreases.

It remains the same

2. If an electron is to escape from a one-dimensional, finite well by absorbing a photon, which is true?

The photon’s energy must equal the difference between the electron’s initial energy level and the bottom of the nonquantized region.

The photon’s energy must equal the difference between the electron’s initial energy level and any energy value in the nonquantized region.

The photon’s energy must equal the difference between the zero energy level and the bottom of the nonquantized region.

3. If two quantum states are degenerate, which is true?

They have identical wave functions.

They have identical momenta.

They have identical energies.

4. Which is true about the energy levels of hydrogen?

Their spacing increases as we move up through the levels.

They are evenly spaced.

Their spacing decreases as we move up through the levels.

5. Which is true?

A series is the collection of jumps to and from a particular level and any higher level. A series limit is the greatest such jump.

A series is the collection of jumps to and from a particular level and any lower level. A series limit is the greatest such jump.

A series is the collection of jumps to and from a particular level and any higher level. A series limit is the smallest such jump.

A series is the collection of jumps to and from a particular level and any lower level. A series limit is the smallest such jump.

6. For hydrogen in ground state, at what radius does the radial probability density have a maximum?

zero

at the Bohr radius

at twice the Bohr radius

at infinite distance

7. What does the square of the normalized wave function give us?

the probability of the electron being detected

the probability per unit length of the electron being detected

the probability per unit area of the electron being detected

the probability per unit volume of the electron being detected

Answer 1

1. Increases, 2. energy from the initial level to some state of the unbound zone, 3. They have identical energies. 4. space increases as we go through the levels , 5. The series is the jumps from one level to each of the superiors and the limit is up to the level n = ∞. 6. Bohr radius

Step-by-step explanation:

1) the function of the wave function of an electron in an infinite quantum well is

φ = A sin (n ππ x / L)

The probability density is

P = φ*φ

P = A² sin² (n π x / L)

Points with maximum probability occur when the sine function is maximum, so the argument must be ±π / 2

.n π x / L = π / 2

.n = L / 2x

Where x goes from zero to L

When n = 1 there is only one value of x, so there is only one maximum

For n = 2 there are two values ​​of x, there are two maximums

For n = 3 there are three values ​​of x, there are three maximums

We can see that increasing the quantum number increases the number of maximums linearly.

Answer is increment

2) To escape from the potential well this is that the atom is ionized must acquire energy from the initial level to some state of the unbound zone (quantized)

3) A state is degenerate is that for several wave functions you have the same energy

4) The expression for energy in a potential well is

E = (h² / 8mL²) n²

We see that the separation in energy increases quadratically with the quantum number

The answer is: space increases as we go through the levels

5) the first answer is True

The series is the jumps from one level to each of the superiors and the limit is up to the level n = ∞

6) the fundamental state is the one with the smallest size. The smallest radius of the hydrogen atom is the Bohr radius

.ao = 0.5 nm

.7) The probability density. This is the probability of finding the electron in a given region of space. The answer is: the probability per unit volume that the electron is detected