What is the threshold wavelength in $nm$ for a metal with a work function of $4.0 \ eV$?

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.

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light rays $(v_1 > v_2)$. If the maximum kinetic energies of the photoelectrons emitted in the two cases are in the ratio of $k : 1$, then what is the threshold frequency of the metallic surface?

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?

Which of the following graphs represents the variation of stopping potential $(V_0)$ with the frequency $(\nu)$ of incident light for a photoelectric cell?

The ratio of work functions of two metals $A$ and $B$ is $1:2$. If radiations of frequencies $f$ and $2f$ are incident on the surfaces of $A$ and $B$ respectively,the ratio of the maximum kinetic energies of the emitted photoelectrons will be: (Given $f >$ threshold frequency of $A$ and $2f >$ threshold frequency of $B$)