Use the following equation:

Where is the rest length,

is the velocity of the object

is the speed of light

is the observed length

Plugging in values

Using

Plugging in values

Using

Plugging in values

Use the following equation:

Where is the rest length,

is the velocity of the object

is the speed of light

is the observed length

Plugging in values

The ejection of electrons from a metal is known as the photoelectric effect. In fact, it was a key discovery that led to the acceptance of the particle nature of light, because the wave nature of light could not account for this finding.

The key that allowed scientists to find this out was that the speed of electrons ejected from the metal was dependent on the color of the light. The intensity of light had no effect on the speed at which electrons were ejected.

As a part of developing this theory, scientists referred to individual discrete particles of light as photons. In order to eject electrons from the metal, individual photons needed to have a sufficient amount of energy. The intensity of light (with a greater amplitude of its waves) represents a case in which photons are striking the metal at a greater rate. But, the individual energy of the photons could be too low in such a situation, hence why intensity is not the key property here. Instead, a higher frequency of light allows each individual photon to have greater energy - enough to knock the metal's electrons off. Furthermore, as the frequency of the light increases, the energy of the individual photons increases and the kinetic energy of the ejected electrons increases as well. The expression for the energy of a photon is shown as follows.

Using

Plugging in values

The energy difference between the second excited state and the ground state will be equal to the photon energy since energy is conserved.

Since the energy difference is in electron volts, they need to be converted to Joules. Another convenient formula is to notice that since and are constants, they can be converted to electron volts and you can use

The ejection of electrons from a metal is known as the photoelectric effect. In fact, it was a key discovery that led to the acceptance of the particle nature of light, because the wave nature of light could not account for this finding.

The key that allowed scientists to find this out was that the speed of electrons ejected from the metal was dependent on the color of the light. The intensity of light had no effect on the speed at which electrons were ejected.

As a part of developing this theory, scientists referred to individual discrete particles of light as photons. In order to eject electrons from the metal, individual photons needed to have a sufficient amount of energy. The intensity of light (with a greater amplitude of its waves) represents a case in which photons are striking the metal at a greater rate. But, the individual energy of the photons could be too low in such a situation, hence why intensity is not the key property here. Instead, a higher frequency of light allows each individual photon to have greater energy - enough to knock the metal's electrons off. Furthermore, as the frequency of the light increases, the energy of the individual photons increases and the kinetic energy of the ejected electrons increases as well. The expression for the energy of a photon is shown as follows.

Using

Plugging in values

The energy difference between the second excited state and the ground state will be equal to the photon energy since energy is conserved.

Since the energy difference is in electron volts, they need to be converted to Joules. Another convenient formula is to notice that since and are constants, they can be converted to electron volts and you can use