The wavelength of the bright red line in the spectrum of atomic
hydrogen is 652 nm. what is the energy of the photon generated in
the transition?

The energy of the photon generated in the transition is 3.14*10⁻¹⁹ J

Explanation:

There are two equation that we need to use in order to solve this problem:

The first one is Planck's equation, which describes the relationship between energy and frequency:

E = h*v    eq. 1)

Where E is energy, h is Planck's constant (6.626 * 10⁻³⁴ J*s) and v is the radiation frequency.

In order to know the frequency, we use the second equation, which is the wave equation:

c = λ*v    eq. 2)

Where c is the speed of light in vacuum (aprx 3 * 10⁸ m/s), and λ is the wavelength. If we solve that equation for v we're left with

v=c/λ    eq. 3)

We replace v in eq. 1):

E= c*h/λ

Lastly we put the data we know and solve the equation, keeping in mind the correct use of units (converting 652 nm into m):