Two of the wavelengths emitted by a hydrogen atom are 97.26 nm and 1282 nm . part a what is the m value for the wavelength 97.26 nm ? express your answer as an integer. part b what is the n value for the wavelength 97.26 nm ? express your answer as an integer. part c what is the m value for the wavelength 1282 nm ? express your answer as an integer. part d what is the n value for the wavelength 1282 nm ? express your answer as an integer.part e part complete for the wavelength 97.26 nm , is the light infrared, visible, or ultraviolet? part f part complete for the wavelength 1282 nm , is the light infrared, visible, or ultraviolet?

A) m = 4

We can solve the problem by using Rydberg equation:

where

is the Rydberg constant for hydrogen

n is the principal quantum number of the upper energy level

m is the principal quantum number of the lower energy level

For the first wavelength, we have

Substituting into the equation, we find

)

By setting n=1, we obtain the Lyman series which goes from 121.6 nm (for m=2) to 91.18 nm (for ). So our line of 97.26 nm must be in this series.

By setting n=1, we find m:

B) n = 1

n can be found by thinking about the limit of the different series.

Larger n corresponds to larger wavelengths; for each n, m goes from (n+1) to , and the shortest wavelength of each series is the one corresponding to .

If we put n = 2, and , we find the shortest wavelength of the n=2 series:

which is longer than our line at 97.26 nm, so n must be smaller than 2, which means n=1.

C) m = 5

Similarly to what we did in part A), here we have a wavelength of

Substituting into the Rydberg equation, we find

)

By setting n=3, we obtain the Paschen series which goes from 1875 nm (for m=4) to 820.4 nm (for ). So our line of 1282 nm must be in this series.

By setting n=3, we find m:

D) n = 3

Similarly to what we did in part B), if we put n = 4, and , we find the shortest wavelength of the n=4 series:

which is longer than our line at 1282 nm, so n must be smaller than 4. Indeed, if we try with n=3, we find:

So, our line is contained in the n=3 series.

E) Ultraviolet

We can answer this question by looking at the different wavelengths of the electromagnetic spectrum. In fact, we have:

Ultraviolet: 380 nm - 1 nm

Visible: 750 nm - 380 nm

Infrared: 1 mm - 750 nm

Our wavelength here is

97.26 nm

So, we see it is included in the ultraviolet part of the spectrum. In fact, all lines in the Lyman series (n=1) lie in the ultraviolet ragion.

F) Infrared

Again, the electromagnetic spectrum is:

Ultraviolet: 380 nm - 1 nm

Visible: 750 nm - 380 nm

Infrared: 1 mm - 750 nm

Our wavelength here is

1282 nm

So, we see it is included in the infrared part of the spectrum. In fact, all lines in the Paschen series (n=3) lie in the infrared band.

The correct answer is weight.

The weight is the measure of the how much the gravity pulls a body or mass on the planet. There lies a difference in the weight of the body on the moon and the weight of the body on earth. This is because there is a difference in the value of gravity on earth and moon.This is the reason, the mass of the body remains same everywhere but the weight of the body changes because the gravity acts on it.

Gravity adds weight to the body.