Question

What is the energy of an electron in a Li+ ion when an electron moves from n = 2 to n =3?

Answer 1

Answer:

The question wants you to determine the energy that the incoming photon must have in order to allow the electron that absorbs it to jump from

n

i

=

2

to

n

f

=

6

.

A good starting point here will be to calculate the energy of the photon emitted when the electron falls from

n

i

=

6

to

n

f

=

2

by using the Rydberg equation.

1

λ

=

R

⋅

(

1

n

2

f

−

1

n

2

i

)

Here

λ

si the wavelength of the emittted photon

R

is the Rydberg constant, equal to

1.097

⋅

10

7

m

−

1

Plug in your values to find

1

λ

=

1.097

⋅

10

7

.

m

−

1

⋅

(

1

2

2

−

1

6

2

)

1

λ

=

2.4378

⋅

10

6

.

m

−

1

This means that you have

λ

=

4.10

⋅

10

−

7

.

m

So, you know that when an electron falls from

n

i

=

6

to

n

f

=

2

, a photon of wavelength

410 nm

is emitted. This implies that in order for the electron to jump from

n

i

=

2

to

n

f

=

6

, it must absorb a photon of the same wavelength.