Dual Nature of Radiation and Matter

[h] = ML²T^-1

[E] = ML²T^-2

[V] = ML²T^-2C^-1

[P] = MLT^-1

K = qV

$p=\sqrt[]{2mk}=\sqrt[]{2mqV}$

$\lambda =\frac{h}{p}=\frac{h}{\sqrt[]{2mqV}}$

$\frac{{\lambda }_p}{{\lambda }_{\alpha }}=\sqrt[]{\frac{m_{\alpha }}{m_p}.\frac{q_{\alpha }}{q_p}}=\sqrt[]{4*2}=2*1.4=2.8$

Energy corresponding to a particle is mc²

$\frac{hc}{\lambda }=m{c}^2\Rightarrow \frac{hc}{\lambda }=\left(\frac{x}{3}h\right)c^2\Rightarrow x=\frac{3}{\lambda c}=\frac{3}{10*10^{-10}*3*10^8}$ = $\frac{1}{10^{-1}}=10$

Using de-Broglie equation for wave nature of particle :

$\lambda =\frac{hc}{mv}\Rightarrow \lambda \alpha \frac{1}{m}$

$\frac{{\lambda }_e}{{\lambda }_P}=\frac{\frac{1}{m_e}}{\frac{1}{m_P}}=\frac{m_P}{m_e}=1836$

Stopping potential defined in terms of wavelength as :

$eV=\frac{hc}{\lambda }-?\Rightarrow 0.710eV=\frac{hc}{491}-?\Rightarrow 1.43eV=\frac{hc}{\lambda }-?$

Using above two equation we can calculate :

$\lambda =382nm$

(A) If $c$  is the velocity of light

so,   $E=h\nu$   (Energy of photon)

(B) Velocity of photon is equal to velocity of light i.e. c.

(C)  $\lambda =\frac{h}{p}$

$p=\frac{h}{\lambda }$

$p=\frac{hv}{c}$

(D) In photon-electron collision both total energy and total momentum are conserved.

In the case for maximum elongation,

Stress = Elastic limit

${\delta }_{max}=\frac{{\sigma }_{elastic }*L}{ Young\text{'}s modulus }=\frac{8*10^8*1}{2*10^{11}}=4*10^{-3}$

$=4 mm$

i.e. maximum elongation is 4 mm

$E=IA$

$=100*1*10^{-4}$

$=10^{-2}W$

$E=nh\frac{c}{\lambda }$

$10^{-2}=\stackrel{?}{n}*\frac{6.64*10^{-34}*3*10^8}{900*10^{-9}}$

$\stackrel{?}{n}=\frac{10^{-2}*9*10^{-7}}{6.64*10^{-34}*3*10^8}$

$\stackrel{?}{n}=4.5*10^{16}$

de-Broglie wavelength $\lambda =\frac{h}{P}=\frac{h}{mv}=\frac{h}{\sqrt[]{2mE}}$ where $E=\frac{1}{2}m{v}^2$

Squaring both sides,

${\lambda }^2=\frac{h^2}{4m^{2}E}$

$\Rightarrow \frac{1}{{\lambda }^2}=\left( constant \right)E$

Graph passes through origin with constant slope.

In solar cells, electron emission converts the light energy into electrical energy through the photoelectric effect. Solar cells work due to photoelectric effect, in which photons from sunlight strike solar cell surface. When a photon that has sufficient energy hits the surface, it transfers its energy to an electron in the material of solar cell surface. This causes the electron emission from its bound state. Solar cells can use photoelectric effect to generate electron-hole pairs that are separated and collected for producing electrical current. This provides a renewable source of power.