Atomic Structure - Result Question 97
####73. (a) The Schrodinger wave equation for hydrogen atom is
$$ \psi _{2 s}=\frac{1}{4(2 \pi)^{1 / 2}}\left(\frac{1}{a _0}\right)^{3 / 2}\left(2-\frac{r}{a _0}\right) e^{-r / 2 a _0} $$
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, $\psi^{2}$ must vanishes, i.e.
$$ \begin{aligned} \psi _{2 s}^{2} & =0=\left[\frac{1}{4 \sqrt{2} \pi}\right]^{2}\left(2-\frac{r _0}{a _0}\right)^{2} e^{-\frac{r _0}{a _0}} \ \Rightarrow \quad 2-\frac{r _0}{a _0}=0 & \Rightarrow r _0=2 a _0 \ \text { (b) } \quad \lambda=\frac{h}{m v} & =\frac{6.625 \times 10^{-34}}{100 \times 10^{-3} \times 100}=6.625 \times 10^{-35} m \ & =6.625 \times 10^{-25} \AA \text { (negligibly small) } \end{aligned} $$
