\(E=\frac{12400 \stackrel{o}A}{4100 \stackrel{o}A}=3.02 eV\)

\(\lambda_0  =\frac{h c}{\phi}  \)
\(=\frac{6.626 \times 10^{-34} \times 3 \times 10^8}{3.313 \times 1.6 \times 10^{-19}}  \)
\( =\frac{19.8782400}{5.3} \times 10^{-7}  \)
\(\lambda_0  =3.750 \times 10^{-7} \simeq 3750 \stackrel{o}A\)

\(\lambda\propto \frac{1}{\sqrt{V}}\)
\(\frac{\lambda_1}{\lambda_2}=\frac{\sqrt{224\times10^3}}{\sqrt{14\times 10^3}}\)
\(=\sqrt{16}=4\)
\(\lambda_{\mathrm{2}}= \frac{\lambda_1}{4}\)

The resistance of the semiconductor changes in accordance with the radiant energy incident on it.

Sensitive element made of semiconductor is used which generates voltage proportional to the intensity of light or other radiations.

The de Broglie wavelength associated with the kinetic energy k is given as \(\lambda=\frac{h}{\sqrt{2 m k}}\) , where m is the mass of the particle.
Therefore \(\lambda_{\mathrm{e}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{~m}_{\mathrm{e}} \mathrm{k}_{\mathrm{e}}}} \text { and } \lambda_{\alpha}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{~m}_{\alpha} \mathrm{k}_{\alpha}}} \text {. But } \mathrm{k}_{\mathrm{e}}=\mathrm{k}_{\alpha} . \)
Therefore \(\frac{\lambda_{\mathrm{e}}}{\lambda_{\alpha}}=\sqrt{\frac{\mathrm{m}_{\alpha}}{\mathrm{m}_{\mathrm{e}}}} \mathrm{m}_{\alpha}>\mathrm{m}_{\mathrm{e}^{*}} \text {. Therefore, } \lambda_{\mathrm{e}}>\lambda_{\alpha^{\circ}}\)

Photo cell is a device which converts light energy into electrical energy. It works on the principle of photo electric effect. When light is incident on photosensitive materials, their electric properties will get affected, based on which Photo cells are classified into three types. They are
(i) Photo emissive cell
(ii) Photo voltaic cell
(iii) Photo conductive cell

The photocurrent, (ie. the number of electrons emitted per second) is directly proportional to the intensity of the incident light.

i) When a fast-moving electron penetrates and approaches a target nucleus, the interaction between the electron and the nucleus either accelerates or decelerates it which results in a change of path of the electron.
ii) The radiation produced from such decelerating electrons is called Bremsstrahlung or braking radiation.

iii) The energy of the photon emitted is equal to the loss of kinetic energy of the electron
iv) Since an electron may lose part or all of its energy to the photon, the photons are emitted with all possible energies (or frequencies).
v) The continuous x-ray spectrum is due to such radiations
vi) When an electron gives up all its energy, then the photon is emitted with the highest frequency v_o (or lowest wavelength \(\lambda\)_o).
vii) The initial kinetic energy of an electron is given by eV where V is the accelerating voltage. Therefore, we have
\({ hv }_{ 0 }=eV(or)\frac { hc }{ { \lambda }_{ 0 } } =eV\)
\(\\ { \lambda }_{ 0 }=\frac { hc }{ eV } \)
viii) Where \({ \lambda }_{ 0 }\) is the cut-off wavelength. Substituting the known values in the above equation, we get
\({ \lambda }_{ 0 }=\frac { 12400 }{ V } \)Å    ...(1)
The relation given by equation (1) is known as the Duane - Hunt formula.
ix) The value  \({ \lambda }_{ 0 }\)depends only on the accelerating potential and is the same for all targets.
x) This is in good agreement with the experimental results.
xi) Thus, the production of continuous x-ray spectrum and the origin of cut-off wavelength can be explained on the basis of the photon theory of radiation.

Construction:
(i) It consists of an evacuated glass or quartz bulb in which two metallic electrodes - that is, a cathode and an anode are fixed.
(ii) The cathode C is semi-cylindrical in shape and is coated with a photo sensitive material.
(iii) The anode A is a thin rod or wire kept along the axis of the semi-cylindrical cathode.
(iv) A potential difference is applied between the anode and the cathode through a galvanometer G.

Working:
When cathode is illuminated, electrons are emitted from it. These electrons are attracted by anode and hence a current is produced which is measured by the galvanometer. For a given cathode, the magnitude of the current depends on
(i) The intensity to incident radiation and
(ii) The potential difference between anode and cathode.

Explanation for the photoelectric effect:
The experimentally observed facts of photoelectric effect can be explained with the help of Einstein's photoelectric equation.
(i) As each incident photon liberates one electron, then the increase of intensity of the light (the number of photons per unit area per unit time) increases the number of electrons emitted thereby increasing the photocurrent. The same has been experimentally observed.
(ii) From K_max = hv - Φ_0, it is evident that K_max is proportional to the frequency of the light and is independent of intensity of the light.
(iii) As given in equation \({ hv }_{ o }+\cfrac { 1 }{ 2 } { mv }^{ 2 }\) , there must be minimum energy (equal to the work function of the metal) for incident photons to liberate electrons from the metal surface. Below which, emission of electrons is not possible. Correspondingly, there exists minimum frequency called threshold frequency below which there is no photoelectric emission.
(iv) According to quantum concept, the transfer of photon energy to the electrons is instantaneous so that there is no time lag between incidence of photons and ejection of electrons.
Thus, the photoelectric effect is explained on the basis of quantum concept of light.

From Einstein's photoelectric equation, stopping potential V_o is
eVo = hv - hv_o V_o = \(\frac{h}{e}(v-v_o)\)
Given > v_o, so with increase of frequency v, stopping potential increases.

de Broglie wavelength (\(\lambda\)) is given is \(\lambda\) = \(\frac{h}{m}\)
Given v_p = v_e
where v_p = velocity 
v_e = velocity of electron
Since m_p > m_e
From the given relation 
\(\lambda \alpha \frac { 1 }{ m } ,hence\quad { \lambda }_{ p }<{ \lambda }_{ e }\) 

\(\lambda=4000 \stackrel{o}A=4000 \times 10^{-10} \mathrm{~m} \)
\(\lambda=\frac{\mathrm{h}}{\mathrm{mv}}\Rightarrow \mathrm{v }=\frac{\mathrm{h}}{\mathrm{m\lambda}}=\frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 4000 \times 10^{10}}=1820 \mathrm{~ms}^{-1} \)