Question

An electron tube was sealed off during manufacture at a pressure of 1 × 10^–7 torr at 27°C. Its volume is 100 cm³. The number of molecules that remain in the tube is­­­­­_______(density of mercury is 13.6 gcm^–3) (1 torr = 133 Pa) 

(A) 3.9 × 10¹¹ 

(B) 3 × 10¹⁶ 

(C) 2 × 10¹⁴ 

(D) 7 × 10¹¹

Answer 1

Correct option: (A) 3.9 × 10¹¹

Explanation:

Given: P = 1.2 × 10^–7 torr = 1.2 × 10^–7 × 133 -------- as 1 torr = 133 Pa

= 159.6 × 10^–7 Pa = 159.6 × 10^–7 N/m² 

V = 100 cm³ = 100 × 10^–6 m³ 

T = 27°C = 300 k

As PV = NK_BT

∴ N = No of molecules = {(PV) / (K_BT)}

= {(159.6 × 10^–7 × 100 × 10^–6) / (1.38 × 10^–23 × 300)}

= 0.385 × 10⁺¹² 

= 3.85 × 10¹¹