Speed of an electron in Bohr's 7 text th orbit for Hydrogen atom is 3.6 × 106 m / s. The corresponding speed of the electron in 3 text rd orbit, in m / s is :

Question

Speed of an electron in Bohr's 7 text th orbit for Hydrogen atom is 3.6 × 106 m / s. The corresponding speed of the electron in 3 text rd orbit, in m / s is : (A) (3.6 × 106) (B) (7.5 × 106) (C) (1.8 × 106) (D) (8.4 × 106)

Tardigrade Admin · Accepted Answer

V n propto ( Z / n ) Z =1, ∴ V n propto (1/ n ) ∴ ( V 3/ V 7)=(7/3) ∴ V 3=(7/3) V 7 =(7/3) × 3.6 × 106 m / s =8.4 × 106 m / s

Q. Speed of an electron in Bohr's $7^{th}$ orbit for Hydrogen atom is $3.6 \times 1 0^{6} m / s$ . The corresponding speed of the electron in $3^{rd}$ orbit, in $m / s$ is :

$(3.6 \times 1 0^{6})$

$(7.5 \times 1 0^{6})$

$(1.8 \times 1 0^{6})$

$(8.4 \times 1 0^{6})$

$V_{n} \propto \frac{Z}{n}$
$Z = 1,$
$∴ V_{n} \propto \frac{1}{n}$
$∴ \frac{V _{3}}{V _{7}} = \frac{7}{3}$
$∴ V_{3} = \frac{7}{3} V_{7}$
$= \frac{7}{3} \times 3.6 \times 1 0^{6} m / s$
$= 8.4 \times 1 0^{6} m / s$

Q. Speed of an electron in Bohr's 7th orbit for Hydrogen atom is 3.6×106m/s. The corresponding speed of the electron in 3rd orbit, in m/s is :

(3.6×106)

(7.5×106)

(1.8×106)

(8.4×106)