Question

Which of the air pressures is appropriate for the production of cathode rays in the discharge tube?
$\eqalign{
  & A.1cmHg \cr
  & B.1mmHg \cr
  & C.0.001cmHg \cr
  & D.0.001mmHg \cr} $

Answer 1

Hint: Cathode rays are nothing but the electron beam travelling from negatively charged electrode(cathode) to positively charged electrode(anode) in discharge tube. In the travelling path there should be no obstacles. If there are any obstacles in the way which electrons are travelling, electrons cannot reach the anode. Based on this information we can answer the question.

Formula used:
$PV = nRT$

Complete answer:
In case of photoelectric effect, the cathode is hit by a beam of photons which causes electrons in the cathode to come out of the cathode and go to anode. Potential difference is maintained between cathode and anode.
Now gas will be present in that discharge tube
According to ideal gas equation
     $PV = nRT$
Where
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = universal gas constant
T = Temperature of the gas
Now at constant temperature and volume if pressure is increased then number of moles get increased which inturn increases number of atoms i.e more obstacles will be present for the electron path
So lower pressures are always favoured for the production of cathode rays.
The lowest pressure in the given options is 0.001mm Hg

So, the correct answer is “Option D”.

Note:
There is no fixed value for pressure in the discharge tube. Generally low pressures are always preferred. Hence if there is another option which is lower than 0.001mm Hg that would have become the answer for this question. So find out the lowest pressure value of all the options and mark it as an answer. The gas used in the discharge tube would be inert gas to avoid any chemical interaction with electrons. More over 76cm Hg = $1.013 \times 10^5$ pascal.