Match the following Column-I with Column-II

Column-I		Column-II
A	In a sample of H-atom for $5\to 2$ transition	P	Maximum 6 spectral lines will be observed from the sample
B	In a sample of $H{e}^{+}$ion for $5\to 1$ transition	Q	A photon of wavelength $\lambda =\frac{36}{5R}$ can be emitted
C	In a sample of H-atom for $7\to 3$ transition	R	A photon of wave number $\overline{v}=\frac{7R}{144}$ can be emitted
D	In a sample of $H{e}^{+}$-ion for $7\to 4$ transition	S	When single isolated atom/ ion is considered maximum 4 spectral lines are observed for given transition
		T	At least one photon is visible

(A) For $5\to 2$  transition in H-atom sample
Max.spectral lines   $=\frac{\Delta n(\Delta n+1)}{2}=\frac{3\times 4}{2}=6$
$\lambda$  of option corresponding to $3\to 2$ transition: $\frac{1}{\lambda }=R{\left(1\right)}^2$
 $[\frac{1}{2^2}-\frac{1}{3^2}]\therefore \lambda =\frac{36}{5R}$
  $\overline{v}$  of photon corresponding to $4\to 3$  transition:  $\overline{v}=R{\left(1\right)}^2$
 $[\frac{1}{3^2}-\frac{1}{4^2}]\therefore \overline{v}=\frac{7R}{144}$
For single isolated  atom, maximum spectral lines  $=3(5\to 4,4\to 3,3\to 2)$
(B) For  $5\to 1$ transition in $H{e}^{+}$  ion sample
Max.spectral lines  $=\frac{n(n-1)}{2}=\frac{5\times 4}{2}=10$
${\left(H\right)}_{3\to 2}={\left(H{e}^{+}\right)}_{6\to 4}$  (Not possible for given sample)
${\left(H\right)}_{4\to 3}={\left(H{e}^{+}\right)}_{8\to 6}$ (Not possible for given sample)
For single isolated ion, maximum spectral lines = 

$=4(5\to 4,4\to 3,3\to 2,2\to 1)$
(C) For $7\to 3$ transition in H atom sample
Max. spectral lines= $\frac{(4+1)\times 4}{2}=10$
To emit photon of $\lambda =\frac{36}{5R}$ , transition should be from  $3\to 2$ (Not possible)
To emit photon of  $\overline{v}=\frac{7R}{144}$  transition should be from  $4\to 3$ ( possible)
For single isolated atom, maximum spectral lines=  

$4(7\to 6,6\to 5,5\to 4,4\to 3)$
(D)  For $7\to 4$  transition in $H{e}^{+}$  ion sample 
Max. Spectral lines  $\frac{(3+1)\times 3}{2}=6$
${\left(H\right)}_{3\to 2}={\left(H{e}^{+}\right)}_{6\to 4}$ (possible for given sample)
$\therefore$  photon of $\lambda =\frac{36}{5R}$ , can be emitted
 ( Not possible for given sample)
For single isolated ion, maximum spectral lines = $3(7\to 6,6\to 5,5\to 4)$
Any photo whose energy is 1.55 to 3.1 ev, will be visible