What is the energy of a photon that has the same wavelength as a 12-eV electron? (h = 6.63 × 10-34 J×s)

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To find the energy of a photon with the same wavelength as a 12-eV electron, we can use the relationship between energy and wavelength for photons.

The energy of a photon can be calculated using the equation:

E = hc/λ

Where:
E is the energy of the photon
h is the Planck's constant (6.63 × 10^(-34) J×s)
c is the speed of light in a vacuum (3 × 10^8 m/s)
λ is the wavelength of the photon

First, we need to convert the electron volts (eV) to joules (J). The conversion factor is 1 eV = 1.6 × 10^(-19) J.

So, the energy of a 12-eV electron is:
E = 12 eV × 1.6 × 10^(-19) J/eV
= 1.92 × 10^(-18) J

Next, we can substitute the values into the equation to find the wavelength of the photon:

1.92 × 10^(-18) J = (6.63 × 10^(-34) J×s) × (3 × 10^8 m/s) / λ

Rearranging the equation to solve for λ:

λ = (6.63 × 10^(-34) J×s) × (3 × 10^8 m/s) / (1.92 × 10^(-18) J)

Calculating λ:

λ = 9.922 × 10^(-7) m

Therefore, the energy of a photon with the same wavelength as a 12-eV electron is 1.92 × 10^(-18) J, and the wavelength is approximately 9.922 × 10^(-7) m.

To find the energy of a photon that has the same wavelength as a given electron, you can use the equation:

Energy of a photon = Planck's constant (h) × speed of light (c) / wavelength

Given that the energy of the electron is 12 eV, we need to convert it to joules since Planck's constant is given in joules. The conversion factor is 1 eV = 1.6 × 10^-19 joules.

So, the energy of the electron in joules would be:
12 eV × 1.6 × 10^-19 J/eV = 1.92 × 10^-18 J

Now, let's assume the wavelength of the photon is equal to the wavelength of the electron. We'll use the energy of the electron to find the energy of the photon.

The equation becomes:
Energy of a photon = (Planck's constant × speed of light) / wavelength

Substituting the given values:
Energy of a photon = (6.63 × 10^-34 J·s × 3 × 10^8 m/s) / wavelength

To solve for the wavelength, we rearrange the equation:
wavelength = (Planck's constant × speed of light) / Energy of a photon

Plugging in the values:
wavelength = (6.63 × 10^-34 J·s × 3 × 10^8 m/s) / 1.92 × 10^-18 J

Calculating this gives us the wavelength of the photon.

convert 12 eV to joules, then

E=hc/lambda