Number of Wavelengths Emitted from Excited Atomic Hydrogen Level 4

[aurao2003]

Homework Statement

hi
i came across this problem on an aqa physics a past question.

How many different wavelengths of electromagnetic radiation can be emitted after
atomic hydrogen is excited to level 4?

Homework Equations

The Attempt at a Solution

i was looking at transitions from level 4 to the ground. i obtained 10 but the answer suggested 6. this was my conclusion;
from level 4 (4 wavengths. this was calculating from 4 to 3, 4 to 2, 4 to 1 etc)
i calculated in this manner for level 3 to the ground, 2 to the ground state etc.
can someone kindly clarify where i am going wrong?
thanks

 

[Sourabh N]

How did you get 10? Count again?

 

[zorro]

The formula for it is n(n-1)/2 where 'n' is the energy level from where it is excited.
You can derive it using Combinations.

 

[Redbelly98]

.
.
.
from level 4 (4 wavengths. this was calculating from 4 to 3, 4 to 2, 4 to 1 etc)
.
.
.

You have only listed 3 wavelengths, not 4:

4→3
4→2
4→1​

 

[SammyS]

Homework Statement

hi
i came across this problem on an aqa physics a past question.

How many different wavelengths of electromagnetic radiation can be emitted after
atomic hydrogen is excited to level 4?

Homework Equations

The Attempt at a Solution

i was looking at transitions from level 4 to the ground. i obtained 10 but the answer suggested 6. this was my conclusion;
from level 4 (4 wavelengths. this was calculating from 4 to 3, 4 to 2, 4 to 1 etc)
i calculated in this manner for level 3 to the ground, 2 to the ground state etc.
can someone kindly clarify where i am going wrong?
thanks

A hydrogen atom excited to level 4 may transition to the ground state by emitting radiation by any of the following 4 schemes. $$\displaystyle \lambda_{\,i\,\to 1}$$ is the wavelength emitted as the atom transitions from level i to level j.

$$\displaystyle \lambda_{\,4\,\to 1}$$
$$\displaystyle \lambda_{\,4\,\to 2}$$ followed by $$\displaystyle \lambda_{\,2\,\to 1}$$
$$\displaystyle \lambda_{\,4\,\to 3}$$ followed by $$\displaystyle \lambda_{\,3\,\to 1}$$
$$\displaystyle \lambda_{\,4\,\to 3}$$ followed by $$\displaystyle \lambda_{\,3\,\to 2}$$ followed by $$\displaystyle \lambda_{\,2\,\to 1}$$

$$\displaystyle \lambda_{\,4\,\to 3}$$ and $$\displaystyle \lambda_{\,2\,\to 1}$$, each appear twice in the above. Therefore, there are six different wavelengths which may be emitted.

They are: $$\displaystyle \lambda_{\,4\,\to 1},\ \lambda_{\,4\,\to 2},\ \lambda_{\,4\,\to 3},\ \lambda_{\,3\,\to 1},\ \lambda_{\,3\,\to 2},\ \lambda_{\,2\,\to 1}$$

 

[aurao2003]

thanks a lot everyone. its clear now!