answer the questions below, using lt (for is less than), gt (for is greater than), eq (for equal to), or mi (for more information) in the blanks provided. 1. the wavelength of the photon required to promote an electron in the hydrogen atom from the n = 1 to the n = 3 level is the wavelength of the photon required to promote an electron in the hydrogen atom from the n =1 to the n = 2 level. 2. the energy of a photon with a wavelength of 463 nm is the energy of a photon whose wavelength is 722 nm. 3. in order to promote an electron to go to a higher energy level, light with a wavelength that is 400 nm is required.

1. Given that the wavelength of the photon required to promote an electron in the hydrogen atom from the n = 1 to the n = 3 level is lt the wavelength of the photon required to promote an electron in the hydrogen atom from the n = 1 to the n = 2 level.

2. Given that the energy of a photon with a wavelength of 463 nm is gt the energy of a photon whose wavelength is 722 nm.

3. Therefore, in order to promote an electron to go to a higher energy level, light with a wavelength that is lt 400 nm is required

Explanation:

The equation for electron transition in a hydrogen atom is given by the Rydberg equation as follows;

[tex]\dfrac{1}{\lambda} = R \times \left (\dfrac{1}{n^2_f} - \dfrac{1}{n^2_i} \right )[/tex]

The energy required for electron transition is given by the formula;

[tex]E = \dfrac{h \cdot c}{\lambda}[/tex]

[tex]E = R_E \times \left (\dfrac{1}{n^2_f} - \dfrac{1}{n^2_i} \right )[/tex]

Where;

h = The Planck's constant

λ = The wavelength of light

c = The speed of light

n = Specific energy level

[tex]R_E[/tex] = -2.178 × 10⁻¹⁸ J

Therefore, the energy required to move an electron from one energy level to a higher energy level is inversely proportional to the wavelength of light, λ.

Increase in λ, results in lower energy available to transition to a higher energy level while a decrease in λ results in more energy available to transition to a higher energy level.