Chapter 38: Q. 61 (page 1116)

a. What wavelength photon does a hydrogen atom emit in a $200 \to 199$ transition?
b. What is the difference in the wavelengths emitted in a localid="1650823513478" $199 \to 2$ transition and a $200 \to 2$ transition?

Short Answer

Expert verified

(a) In a transition, wavelength photon a hydrogen atom emit is $λ_{200 \to 199} = 0 .362 m$

(b) The difference in the wave lengths are $Δλ = 0 .368 pm$

Step by step solution

Part (a) Step 1: Given information

The wavelength of hydrogen atom is $200 \to 199$

Part (a) Step 2: Finding emission spectrum wavelength

We can start with an expression for the emission spectrum wavelength.

$λ_{n \to m} = \frac{λ_{0}}{\frac{1}{m^{2}} - \frac{1}{n^{2}}} λ_{200 \to 199} = \frac{91 .18 \cdot 10^{- 9}}{\frac{1}{199^{2}} - \frac{1}{200^{2}}} (200 \to 199 transition) λ_{200 \to 199} = 0 .362 m$

Part (b) Step 1: Given information

The given wavelengths are $199 \to 2$ and $200 \to 2$

Part (b) Step 2: Finding difference between wavelengths

In the same approach, we can figure out $199 \to 2$ transition and $200 \to 2$ transition

localid="1651154009746" $\begin{aligned} λ_{199 \to 2} = \frac{(91 .18 \times 10^{- 9})}{\frac{1}{2^{2}} - \frac{1}{199^{2}}} \\ λ_{200 \to 2} = \frac{(91 .18 \times 10^{- 9})}{\frac{1}{2^{2}} - \frac{1}{200^{2}}} \end{aligned} Δλ = λ_{199 \to 2} - λ_{200 \to 2} (difference between wavelengths) Δλ = \frac{(91 .18 \times 10^{- 9})}{\frac{1}{2^{2}} - \frac{1}{199^{2}}} - \frac{(91 .18 \times 10^{- 9})}{\frac{1}{2^{2}} - \frac{1}{200^{2}}} (substitute) Δλ = 0 .368 pm$

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a. What wavelength photon does a hydrogen atom emit in a $200 \to 199$ transition?
b. What is the difference in the wavelengths emitted in a localid="1650823513478" $199 \to 2$ transition and a $200 \to 2$ transition?

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Finding emission spectrum wavelength

Part (b) Step 1: Given information

Part (b) Step 2: Finding difference between wavelengths

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a. What wavelength photon does a hydrogen atom emit in a 200→199transition?b. What is the difference in the wavelengths emitted in a localid="1650823513478" 199→2transition and a 200→2transition?

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Finding emission spectrum wavelength

Part (b) Step 1: Given information

Part (b) Step 2: Finding difference between wavelengths

One App. One Place for Learning.

Most popular questions from this chapter

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Work Energy and Power

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Study anywhere. Anytime. Across all devices.

a. What wavelength photon does a hydrogen atom emit in a $200 \to 199$ transition?
b. What is the difference in the wavelengths emitted in a localid="1650823513478" $199 \to 2$ transition and a $200 \to 2$ transition?