Question

The clectron in a hydrogen atom, originally in level n=9, undergoes a transition to a lower level by emitting a photon

of wavelength 384 nm. What is the final level of the electron?

Answer 1

To determine the final level of the electron in a hydrogen atom, we can use the equation for the wavelength of a photon emitted during a transition. Rearranging the equation and plugging in the given values, we can solve for the final level of the electron.

Step-by-step explanation:

The electron in a hydrogen atom can undergo a transition to a lower level by emitting a photon of specific wavelength. The wavelength of the photon is related to the energy difference between the initial and final levels. In this case, the electron, initially in level n=9, emits a photon with a wavelength of 384 nm. To determine the final level of the electron, we can use the equation:

1/λ = R*(1/n1^2 - 1/n2^2)

where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final levels, respectively. Rearranging the equation, we have:

n2 = sqrt((1 - λ/R)*(1/n1^2))

Plugging in the values, we find:

n2 = sqrt((1 - 384 nm/R)*(1/9^2))

Therefore, the final level of the electron is found by solving the equation above.