Chapter 37: Q. 4 (page 1081)

Two of the wavelengths emitted by a hydrogen atom are $102.6 n m$ and $1876 n m$ .
a. What are the $m$ and $n$ values for each of these wavelengths?
b. For each of these wavelengths, is the light infrared, visible, or ultraviolet?

Short Answer

Expert verified

a. For $λ = 102.6 n m, n = 3$ and $m = 1$ .

For $λ = 1876 n m, n = 4$ and $m = 3$ .

b. 1) Ultraviolet

2) Infrared

Step by step solution

Part (a) Step 1: Given Information

We have given that wavelengths $λ_{1} = 102.6 n m$ and $λ_{2} = 1876 n m$ .

Part (a) Step 2: Evaluation

Formula for calculating wavelength is given as:

$λ = \frac{91.18}{(\frac{1}{m^{2}} - \frac{1}{n^{2}})} n m$

substituting $λ_{1} = 102.6 n m$

$(\frac{1}{m^{2}} - \frac{1}{n^{2}}) = \frac{91.18}{102.6} = 0.889$

comparing we can see that $m = 1 a n d n = 3$ satisfies the above equation.

substituting $λ_{2} = 1876 n m$

$(\frac{1}{m^{2}} - \frac{1}{n^{2}}) = \frac{91.18}{1876} = 0.0486$

comparing we can see that $m = 3 a n d n = 4$ satisfies the above equation.

Part (b) Step 1: Given information

We have given that wavelengths $λ_{1} = 102.6 n m$ and $λ_{2} = 1876 n m$ .

Part (b) Step 2: Evaluation

$λ_{1}$ has $m = 1$ which corresponds to lyman series and all lines in lyman series lie in ultraviolet region of electromagnetic spectrum.

$λ_{2}$ has $m = 3$ which corresponds to paschen series and all in paschen series lie in infrared region of electromagnetic spectrum.

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Two of the wavelengths emitted by a hydrogen atom are $102.6 n m$ and $1876 n m$ .
a. What are the $m$ and $n$ values for each of these wavelengths?
b. For each of these wavelengths, is the light infrared, visible, or ultraviolet?

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Evaluation

Part (b) Step 1: Given information

Part (b) Step 2: Evaluation

One App. One Place for Learning.

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Two of the wavelengths emitted by a hydrogen atom are 102.6nmand1876nm.a. What are the mand nvalues for each of these wavelengths?b. For each of these wavelengths, is the light infrared, visible, or ultraviolet?

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Evaluation

Part (b) Step 1: Given information

Part (b) Step 2: Evaluation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Wave Optics

Quantum Physics

Solid State Physics

Electrostatics

Space Physics

Study anywhere. Anytime. Across all devices.

Two of the wavelengths emitted by a hydrogen atom are $102.6 n m$ and $1876 n m$ .
a. What are the $m$ and $n$ values for each of these wavelengths?
b. For each of these wavelengths, is the light infrared, visible, or ultraviolet?