SATHEE: Modern Physics 1 Question 36

Modern Physics 1 Question 36

33. The wavelength of light emitted in the visible region by $H e^{+}$ ions after collisions with $H$ atoms is

(a) $6.5 \times 10^{- 7} m$

(b) $5.6 \times 10^{- 7} m$

(d) $4.0 \times 10^{- 7} m$

(2008, 4M)

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Solution:

Visible light lies in the range, $λ_{1} = 4000 \AA$ to $λ_{2} = 7000 \AA$ . Energy of photons corresponding to these wavelengths (in $e V$ ) would be :

$\begin{aligned} E_{1} = \frac{12375}{4000} = 3.09 e V \\ E_{2} = \frac{12375}{7000} = 1.77 e V \end{aligned}$

From energy level diagram of $H e^{+}$ atom, we can see that in transition from $n = 4$ to $n = 3$ , energy of photon released will lie between $E_{1}$ and $E_{2}$ .

$\begin{aligned} Δ E_{43} & = - 3.4 - (- 6.04) \\ = 2.64 e V \end{aligned}$

Wavelength of photon corresponding to this energy,

$\begin{aligned} λ & = \frac{12375}{2.64} \AA = 4687.5 \AA \\ = 4.68 \times 10^{- 7} m \end{aligned}$

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Modern Physics 1 Question 36

33. The wavelength of light emitted in the visible region by He+ions after collisions with H atoms is

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33. The wavelength of light emitted in the visible region by $H e^{+}$ ions after collisions with $H$ atoms is