What is the effect of $SCR$ (Space Charge Region) in a vacuum tube?

The variation of anode current $(I_p)$ in a triode corresponding to a change in grid potential $(V_g)$ at three different values of the plate potential $(V_p)$ is shown in the diagram. The mutual conductance $(g_m)$ of the triode is.........$ m \text{ mho}$.

Why is a vacuum needed in a vacuum tube?

On applying a potential of $-1 \ V$ at the grid of a triode,the following relation between plate voltage $V_p$ $(V)$ and plate current $I_p$ (in $mA$) is found:
$I_p = 0.125 V_p - 7.5$
If on applying $-3 \ V$ potential at the grid and $300 \ V$ potential at the plate,the plate current is found to be $5 \ mA$,then the amplification factor of the triode is:

The plate characteristic curve of a diode in the space charge limited region is as shown in the figure. The slope of the curve at point $P$ is $5.0 \, mA/V$. The static plate resistance of the diode will be ...... $\Omega$.

In a diode valve,the cathode temperature must be ($\phi$ = work function):