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6. In a particular atom, an electron moves from n = 3 to the ground state (n = 1), emitting a photon with frequency 5.2 x 1015 Hz as it does so. What is the difference in energy between n = 3 and n = 1 in this atom? g

User SSAMEERR
by
4.1k points

1 Answer

6 votes

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.

To find the energy of this photon, you can use the Planck - Einstein relation, which looks like this

E

=

h

c

λ

Here

E

is the energy of the photon

h

is Planck's constant, equal to

6.626

10

34

.

J s

c

is the speed of light in a vacuum, usually given as

3

10

8

.

m s

1

As you can see, this equation shows you that the energy of the photon is inversely proportional to its wavelength, which, of course, implies that it is directly proportional to its frequency.

Plug in the wavelength of the photon in meters to find its energy

E

=

6.626

10

34

.

J

s

3

10

8

m

s

1

4.10

10

7

m

E

=

4.85

10

19

.

J

−−−−−−−−−−−−−−−−−

I'll leave the answer rounded to three sig figs.

So, you can say that in a hydrogen atom, an electron located on

n

i

=

2

that absorbs a photon of energy

4.85

10

19

J

can make the jump to

n

f

=

6

.

Step-by-step explanation:

User Harambe
by
3.4k points