Calculate the energy change when an electron moves from n=5 to n=7. Explain/show work please.

E = 1.55 ⋅ 10 − 19 J

Explanation:  

The energy transition will be equal to  1.55 ⋅ 10 − 1 J .  

So, you know your energy levels to be n = 5 and n = 3. Rydberg's equation will allow you calculate the wavelength of the photon emitted by the electron during this transition

1 λ  = R ⋅ ( 1 n 2 final  − 1 n 2 initial  ) , where λ - the wavelength of the emitted photon; R

- Rydberg's constant -  1.0974 ⋅ 10 7 m − 1 ; n final - the final energy level - in your case equal to 3; n initial - the initial energy level - in your case equal to 5. So, you've got all you need to solve for  λ , so 1 λ  =

1.0974 ⋅10  7 m − 1 ⋅ (     −152    

)

1

λ

=

0.07804

⋅

10

7

m

−

1

⇒

λ

=

1.28

⋅

10

−

6

m

Since  

E

=

h

c

λ

, to calculate for the energy of this transition you'll have to multiply Rydberg's equation by  

h

⋅

c

, where

h

- Planck's constant -  

6.626

⋅

10

−

34

J

⋅

s

c

- the speed of light -  

299,792,458 m/s

So, the transition energy for your particular transition (which is part of the Paschen Series) is  

E

=

6.626

⋅

10

−

34

J

⋅

s

⋅

299,792,458

m/s

1.28

⋅

10

−

6

m

E

=

1.55

⋅

10

−

19

J