What is (delta E) for the traansition of an electron from n=9 to n=4 in a Bohr hydrogen atom?

What is the frequency?

Thank you!

dE = 2.18E-18 J*(1/16 - 1/81)

c = freq x wavelength = 3E8 m/s

Thank you!! You are so helpful!

To calculate the energy change (ΔE) for the transition of an electron from one energy level to another in a Bohr hydrogen atom, you can use the formula:

ΔE = - 2.18 x 10^(-18) J * (1/n_final^2 - 1/n_initial^2)

Here, n_final is the final energy level and n_initial is the initial energy level. In this case, the initial energy level (n_initial) is 9, and the final energy level (n_final) is 4.

Substituting these values into the formula:

ΔE = - 2.18 x 10^(-18) J * (1/4^2 - 1/9^2)
= - 2.18 x 10^(-18) J * (1/16 - 1/81)
= - 2.18 x 10^(-18) J * (0.0625 - 0.0123)
= - 2.18 x 10^(-18) J * 0.0502

Using a calculator, the value of ΔE is approximately -1.096 x 10^(-19) J.

To find the frequency (ν), you can use the formula:

ΔE = h * ν

Here, h is the Planck's constant (6.63 x 10^(-34) J·s) and ν is the frequency. Rearranging the formula:

ν = ΔE / h

Substituting the value of ΔE into the formula:

ν = (-1.096 x 10^(-19) J) / (6.63 x 10^(-34) J·s)

Using a calculator, the value of ν is approximately -1.656 x 10^14 Hz. Note that the negative sign indicates that the electron is transitioning to a lower energy level.