Question

If the mass of electron is doubled, then find the new radius (in $\stackrel{o}{A}$) of $1st$ orbit of $H-$atom?
If an electron in $H-$atom jumps from one orbit to other its angular momentum doubles. If the new radius is $x$ times the old radius, then find $x$?

Answer 1

Radius of an $H$ atom is given by,

$r=\frac{n^2{h}^2}{4{\pi }^{2}mZ{e}^2}$

Now $m=2m_e$ i.e. mass of the electron is doubled

Substituting values of $h,m,z=1$ for hydrogen and e the electronic charge r may be calculated as

$r=0.265\times n^2{A}^0$

For $n=1$

$r_o=0.265A^0$ ($r_n$ and $r_o$ are new and old radius)

Now angular momentum is directly proportional to $n$. Hence, for $n=2$ it's angular momentum doubles.

For $n=2$, $r_n=0.265\times \left(2^2\right)A^0$

$r_n=x{r}_o$

$r_n=4r_o$ therefore $x=4$