The maximum velocity of the photoelectrons emitted from the surface is $v$ when light of frequency $n$ falls on a metal surface. If the incident frequency is increased to $3n$,the maximum velocity of the ejected photoelectrons will be:

Einstein received the Nobel Prize for which of the following works?

The threshold frequency of potassium is $3 \times 10^{14} \ Hz$. The work function is ...... .

Match the temperature of a black body given in List-$I$ with an appropriate statement in List-$II$, and choose the correct option.
[Given: Wien's constant as $2.9 \times 10^{-3} \, m-K$ and $\frac{hc}{e}=1.24 \times 10^{-6} \, V-m$ ]

List-$I$	List-$II$
$(P)$ $2000 \, K$	$(1)$ The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function $4 \, eV$
$(Q)$ $3000 \, K$	$(2)$ The radiation at peak wavelength is visible to human eye.
$(R)$ $5000 \, K$	$(3)$ The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction.
$(S)$ $10000 \, K$	$(4)$ The power emitted per unit area is $1/16$ of that emitted by a blackbody at temperature $6000 \, K$.
	$(5)$ The radiation at peak emission wavelength can be used to image human bones.

In a photoelectric effect experiment,$f$ is the frequency of radiations incident on the metal surface and $I$ is the intensity of the incident radiations. Consider the following statements. Which of the following statements are correct?
$(A)$ If $f$ is increased keeping $I$ and work function constant,then the maximum kinetic energy of the photoelectron increases.
$(B)$ If the distance between the cathode and anode is increased,the stopping potential increases.
$(C)$ If $I$ is increased keeping $f$ and work function constant,then the stopping potential remains the same and the saturation current increases.
$(D)$ If the work function is decreased keeping $f$ and $I$ constant,then the stopping potential increases.

Ultraviolet light of wavelength $2271 \,\mathring{A}$ from a $100 \; W$ mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is $-1.3 \; V$, estimate the work function of the metal. How would the photo-cell respond to a high-intensity $(10^{5} \; W \; m^{-2})$ red light of wavelength $6328 \,\mathring{A}$ produced by a $He-Ne$ laser?