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.