Q4. Assertion: a free electron inside a metal needs energy to leave it. Reason: as soon as it starts to leave, the metal surface acquires a positive charge and pulls it back. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: the attraction of the ions holds the electron inside, so it needs at least the work function to escape (NCERT page 275). Strictly, this surface barrier is there even when the metal is neutral or grounded (reasoned from NCERT page 275).
Q5. A proton starts from rest and is accelerated through a potential drop of 1000 V. What is its kinetic energy in eV and in joules?
Its charge equals the electron’s in size, so it gains 1000 eV = 1.602 × 10−16 J (NCERT page 275).
Q6. Thomson found cathode-ray speeds of 0.1 to 0.2 times the speed of light. What range of accelerating voltage does that suggest, ignoring relativity?
The voltage is ½mv2/e. At 3.0 × 107 m/s, ½mv2 ≈ 4.1 × 10−16 J, which is about 2.6 keV, so about 2.6 kV. At twice the speed the energy is four times as much, about 10 kV (reasoned from NCERT page 275).
Q7. How many electrons pass a point each second in a current of 1.0 mA?
n = I/e = (1.0 × 10−3)/(1.602 × 10−19) ≈ 6.2 × 1015 electrons per second (NCERT page 275 for e).