Question

Match the following.

(1)	Energy of ground state of $He^{+}$	(p)	6.04 eV
(2)	Potential energy of 1 orbit of H atom	(q)	-27.2 eV
(3)	Kinetic energy of II excited state of $He^{+}$	(r)	54.4 eV
(4)	Ionisation potential of $He^{+}$	(s)	-54.4 eV

• A. $\left(\right.1\left.\right)-p,\left(\right.2\left.\right)-q,\left(\right.3\left.\right)-r,\left(\right.4\left.\right)-s$
• B. $\left(\right.1\left.\right)-s,\left(\right.2\left.\right)-r,\left(\right.3\left.\right)-q,\left(\right.4\left.\right)-p$
• C. $\left(\right.1\left.\right)-s,\left(\right.2\left.\right)-q,\left(\right.3\left.\right)-p,\left(\right.4\left.\right)-r$
• D. $\left(\right.1\left.\right)-q,\left(\right.2\left.\right)-r,\left(\right.3\left.\right)-p,\left(\right.4\left.\right)-s$

Answer 1

Answer: (C)

Energy of G.S. of $He^{+}=E_{H}\times Z^{2}$
$= - 13.6 \times 4 = - 54.4 \, \text{eV}$
Ionisation potential of $He^{+}=E_{\in fty}-E_{1}$
$= - \left(- 54.4\right) = 54.4 \, \text{eV}$
T.E. of H of 1 orbit $= - 13.6 \, \text{eV}$
2 T.E. = P.E. and $\text{K} \text{.E} = - \text{ T} \text{. E}$
$\text{P} \text{.E} \text{.} \, = - 2 \times 13.6 = - 27.2 \, \text{eV}$
T.E. of H of II excited state $=\frac{- 13.6}{9}\times 4$
of $\text{He} \, = - 6.04 \, \text{eV}$
$\text{K} \text{.E} \text{.} = - \text{(T} \text{.E} \text{.)} = - \left(- 6.04 \, \text{eV}\right) = + 6.04 \, \text{eV}$