SATHEE: Atomic Structure - Result Question 97

Atomic Structure - Result Question 97

####73. (a) The Schrodinger wave equation for hydrogen atom is

$ψ_{2 s} = \frac{1}{4 (2 π)^{1 / 2}} {(\frac{1}{a_{0}})}^{3 / 2} (2 - \frac{r}{a_{0}}) e^{- r / 2 a_{0}}$

where, $a_{0}$ is Bohr’s radius. Let the radial node in $2 s$ be at $r_{0}$ . Then, find $r$ in terms of $a_{0}$ .

(b) A base ball having mass $100 g$ moves with velocity

$100 m / s$ . Find out the value of wavelength of base ball.

(2004, 2M)

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Answer:

Correct Answer: 73. $(63.56 V)$

Solution:

(a) At radial node, $ψ^{2}$ must vanishes, i.e.

$\begin{aligned} ψ_{2 s}^{2} & = 0 = {[\frac{1}{4 \sqrt{2} π}]}^{2} {(2 - \frac{r_{0}}{a_{0}})}^{2} e^{- \frac{r_{0}}{a_{0}}} \Rightarrow 2 - \frac{r_{0}}{a_{0}} = 0 & \Rightarrow r_{0} = 2 a_{0} (b) λ = \frac{h}{m v} & = \frac{6.625 \times 10^{- 34}}{100 \times 10^{- 3} \times 100} = 6.625 \times 10^{- 35} m & = 6.625 \times 10^{- 25} \AA (negligibly small) \end{aligned}$

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Atomic Structure - Result Question 97

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