Question

1. For a hydrogen‑like atom, classify the electron transitions according to whether they result in the absorption or emission of light?n=1 to n=3, n=2 to n=1, n=3 to n=2, n=3 to n=52. Ignoring sign, which transition is associated with the greatest energy change? O n=1 to n=3 O n=2 to n=1 O n=3 to n=2 O n=3 to n=5

Answer 1

Answer:

The transition which is associated with the greatest energy change is from n=1 to n=3.

Explanation:

$E_n=-13.6\times \frac{Z^2}{n^2}ev$

where,

$E_n$ = energy of $n^{th}$ orbit

n = number of orbit

Z = atomic number

Energy of n = 1 in an hydrogen like atom:

$E_1=-13.6\times \frac{Z^2}{1^2}eV=-13.6 Z^2 eV$

Energy of n = 2 in an hydrogen like atom:

$E_2=-13.6\times \frac{Z^2}{2^2}eV=-3.40 Z^2 eV$

Energy of n = 3 in an hydrogen like atom:

$E_3=-13.6\times \frac{Z^2}{3^2}eV=-1.51 Z^2 eV$

Energy of n = 5 in an hydrogen like atom:

$E_5=-13.6\times \frac{Z^2}{5^2}eV=-0.544 Z^2 eV$

1) Energy change transition from n = 1 to n = 3 occurs .

Let energy change be E.

$E=E_3-E_1=-1.51 Z^2 eV-(-13.6 Z^2 eV)=12.09 Z^2 eV$ (absorption)

2) Energy change transition from n = 2 to n = 1 occurs .

Let energy change be E.

$E=E_1-E_2=-13.6 Z^2 eV-(-3.40 Z^2 eV)=-10.2 Z^2 eV$ (emission)

3) Energy change transition from n = 3 to n = 2 occurs .

Let energy change be E.

$E=E_2-E_3=-3.40 Z^2 eV-(-1.51 Z^2 eV)=-1.89 Z^2 eV$(emission)

4) Energy change transition from n = 3 to n = 5 occurs .

Let energy change be E.

$E=E_5-E_3=-0.544 Z^2 eV-(-1.51 Z^2 eV)=0.966 Z^2 eV$ (absorption)

Highest magnitude of energy corresponds to the greatest energy change.So,the transition which is associated with the greatest energy change is from n=1 to n=3.