The energy of a photon with wavelength $\lambda$ is $2 \ eV$. When it strikes a metal surface,the maximum velocity of the emitted photoelectrons is $v$. If the value of $\lambda$ is decreased by $25\%$ and the maximum velocity is doubled,the work function of the metal becomes ...... $eV$.

If the electron in a hydrogen atom jumps from the third Bohr orbit to the ground state directly and the difference between the energies of the two states is radiated in the form of photons. If the work function of the material is $4.1 \text{ eV}$, then the stopping potential is nearly:
$\left[\text{Energy of electron in } n^{\text{th}} \text{ orbit} = \frac{-13.6}{n^2} \text{ eV}\right]$ (in $\text{ V}$)

The light of wavelength $\lambda$ is incident on the surface of a metal with work function $\phi$ and emits electrons. What is the maximum velocity of the emitted electrons? [Given: $m=$ mass of electron,$h=$ Planck's constant,$c=$ velocity of light]

Photons of energy $10 eV$ are incident on a photosensitive surface of threshold frequency $2 \times 10^{15} Hz$. The kinetic energy in $eV$ of the photoelectrons emitted is [Planck's constant $h = 6.63 \times 10^{-34} Js$]. (in $eV$)

When the wavelength of incident radiation on a metal surface is reduced from $\lambda_1$ to $\lambda_2$,the kinetic energy of the emitted photoelectrons is tripled. Find the work function of the metal. [$h =$ Planck's constant,$c =$ velocity of light]

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.