Atomic Structure - Result Question 97
73.
(a) The Schrodinger wave equation for hydrogen atom is
$ \psi _{2 s}=\dfrac{1}{4(2 \pi)^{1 / 2}}\left(\dfrac{1}{a _0}\right)^{3 / 2}\left(2-\dfrac{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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Solution:
- (a) At radial node, $\psi^{2}$ must vanishes, i.e.
$\psi _{2 s}^{2} =0=\left[\dfrac{1}{4 \sqrt{2} \pi}\right]^{2}\left(2-\dfrac{r _0}{a _0}\right)^{2} e^{-\dfrac{r _0}{a _0}} $
$\Rightarrow 2-\dfrac{r _0}{a _0}=0 \Rightarrow r _0=2 a _0 $
(b) $\lambda=\dfrac{h}{m v} =\dfrac{6.625 \times 10^{-34}}{100 \times 10^{-3} \times 100}=6.625 \times 10^{-35} m $
$ =6.625 \times 10^{-25} $ $Å$ (negligibly small)
BETA
