An electron in the hydrogen atom jumps from excited state $n$ to the ground state. The wavelength so emitted illuminates a photosensitive material having work function $2.75 \ eV$. If the stopping potential of the photoelectron is $10 \ V$,then the value of $n$ is

When light of wavelength $300 \ nm$ falls on a photoelectric emitter,photoelectrons are just liberated. For another emitter,light of wavelength $600 \ nm$ is just sufficient for liberating photoelectrons. The ratio of the work function of the two emitters is

The threshold wavelength for the photoelectric effect of a metal is $6500 \mathring{A}$. The work function of the metal is approximately .......... $eV$.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electric potential to the photoemissive substance.
Reason $(R) :$ $A$ negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation.
In the light of the above statements, choose the most appropriate answer from the options given below:

In the case of photoelectric emission from a certain metal,the cutoff frequency is $v$. If radiation of frequency $2v$ is incident on the metal plate,the maximum possible velocity of the emitted electrons will be ($m=$ mass of electron).

An isolated lead ball is charged upon continuous irradiation by $EM$ radiation of wavelength, $\lambda = 221 \,nm$. The maximum potential attained by the lead ball, if its work function is $4.14 \,eV$, is (take, $h = 6.63 \times 10^{-34} \,J \cdot s$, $c = 3 \times 10^8 \,m/s$, $e = 1.6 \times 10^{-19} \,C$): (in $\,V$)