Structure of Atom

Energy of 1 photon = $\frac{hc}{\lambda }$  

Energy of 1 mole of photon =  $N_A\times \frac{hc}{\lambda }$  

$=\frac{6.022\times 10^{23}\times 6.63\times 10^{-34}\times 3\times 10^8}{300\times 10^{-9}}$  

= 0.399 × 10⁶ J = 399 KJ

Only tritium is the isotope of hydrogen which is radioactive in nature that emits low energy b^- particles since its $\frac{n}{p}$ ratio is above stability belt.

Electronic configuration of Ga⁺ ion = [Ar] 3d¹⁰ 4s² 4p⁰

Last electron goes into S-orbital, hence

Azimuthal quantum number $\left(\mathcal{l}\right)$ for last electron = 0

Zn (30) = $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}$  

$Z{n}^{+}=\left[Ar\right]4s^{1}3d^{10}$      

Outermost electron is 4s electron,

$n=4,\mathcal{l}=0,m=0,s=\pm 1/2$         

Ge (Z = 32)

^{$=1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^2$}         

$m_{\mathcal{l}}=0$       (for 4s, 3s, 2s, 1s) 4 orbital

$m_{\mathcal{l}}$       = 0 (one p orbital of 2p and 3p)

$m_{\mathcal{l}}$ = 0 (one d orbital)

Total orbitals = 7

Ans. = 7

mvr = $\frac{nh}{2\pi }\left(angularmomentum\right)$  

$KE=\frac{n^2{h}^2}{8{\pi }^{2}m{r}^2}$ (Bohr’s kinetic energy)

$=\frac{4h^2}{8{\pi }^{2}m{\left(4a_0\right)}^2}\left(n=2\right)$

$K.E.=\frac{1}{32{\pi }^2}\frac{h^2}{m{a}_0^2}$

Comparing with $\frac{h^2}{xm{a}_0^2}$

x = 32π² = 315.50

10x = 3155

According to Bohr’s model, velocity of electron increases according to atomic number (z).

$v_e\propto \frac{z}{n}$ (z = Atomic number and n = number of shell/principal quantum number)

Similarly, velocity of electron decreases according to number of shell (i.e. principal quantum number).

Sequence of sub-energy level decided by the rule of $\left(n+\mathcal{l}\right).$

$\Delta V=2.4\times 10^{-26}m/sec$

And $\Delta x=10^{-7}m$  

According to Heisenberg’s uncertainty

$\Delta v\times \Delta x=\frac{h}{4\pi \times m}$  

$\therefore m=\frac{h}{4\pi \times \Delta v\times \Delta x}=\frac{6.626\times 10^{-34}}{4\times 3.14\times 2.4\times 10^{-26}\times 10^{-7}}$

$\therefore$  m = 0.02198 Kg

Or 21.98 gm

Or 22 gm in the nearest integer.

Value of n & $\mathcal{l}$ $$ can't be same