Question

Which of the following statements are correct?

• A. The total spectral lines obtained from a single line during Zeeman effect is (2l + 1).
• B. In the Lyman series as the energy liberated during transition increases then the distance between the spectral lines goes on decreasing.
• C. The highest probability of finding an electron in 1s orbital is in the vicinity of the circumference.
• D. The highest probability of finding an electron in 1s orbital is exactly at the middle between nucleus and circumference.

Answer 1

Answer: (A)

The total spectral lines obtained from a single line during Zeeman effect is (2l + 1).

Answer 2

The total lines obtained due to the splitting of a spectral line in the presence of magnetic effect is (2l + 1) as the presence of orbitals which have specific orientation in the presence of external field take up certain new orientation. The number of orbitals are equal to (2l + 1) and for each orbital one splitting takes place.

(2) As we move away from the nucleus the difference in the energy levels become lesser and lesser hence.

For 1^st line of Lyman DE = $E_{1}\left\lbrack \frac{1}{n_{1}^{2}}–\frac{1}{n_{n}^{2}} \right\rbrack$

DE₁ = E₁$\left\lbrack \frac{3}{4} \right\rbrack$ – 1^st line; DE₂ = E₁$\left\lbrack \frac{8}{9} \right\rbrack$–2^nd line

DE₃ = E₁$\left\lbrack \frac{15}{16} \right\rbrack$–34^rd line ; DE₄ = E₁$\left\lbrack \frac{24}{25} \right\rbrack$ – 4^th line;

DE₅ = E₁$\left\lbrack \frac{35}{36} \right\rbrack$ – 5^th line;

DE₂ – DE₁ = E₁$\left\lbrack \frac{8}{9}–\frac{3}{4} \right\rbrack$ = E₁$\left\lbrack \frac{5}{36} \right\rbrack$

DE₃ – DE₂ = E₁$\left\lbrack \frac{15}{16}–\frac{8}{9} \right\rbrack$ =

E₁$\left\lbrack \frac{135–128}{144} \right\rbrack$ = E₁$\left\lbrack \frac{7}{144} \right\rbrack$

DE₄ – DE₃ = E₁ $\left\lbrack \frac{24}{25}–\frac{15}{16} \right\rbrack$

= E₁$\left\lbrack \frac{16 \times 24–15 \times 25}{25 \times 16} \right\rbrack$ = E₁ $\left\lbrack \frac{9}{400} \right\rbrack$

We find that (DE₂ – DE₁) > (DE₃ – DE₂)

> (DE₄ – DE₃)

Hence the distance also become lesser and lesser.

(3) The distance from the nucleus for maximum probability of finding electrons is 0.53 Å. This is not on the circumference of the orbital but is in the vicinity of the circumference.