Q: A photoelectric material having work-function \phi_0 is illuminated with light of wavelength \lambda \left(\lambda < \dfrac{hc}{\phi_0}\right) . The fastest photoelectron has a de Broglie wavelength \lambda_d . A change in wavelength of the incident light by \Delta \lambda results in a change \Delta \lambda_d in \lambda_d . Then the ratio \Delta \lambda_d / \Delta \lambda is proportional to

According to photoelectric equation, \dfrac{hc}{\lambda} - \phi =\dfrac{1}{2}mv^2=\dfrac{p^2}{2m}=\dfrac{h^2}{2m\lambda_d^2} \dfrac{-hc}{\lambda^2}\times \Delta \lambda = \dfrac{-h^2}{m\lambda_d^3}\times \Delta \lambda_d \dfrac{\Delta \lambda_d}{\Delta \lambda} \propto \dfrac{ \lambda_d^3}{\lambda^2}

Q: A proton has kinetic energy \mathrm{E}=100\mathrm{k}\mathrm{e}\mathrm{V} which is equal to that of a photon. The wavelength of photon is \lambda_{2} and that of proton is \lambda_{1} . The ratio of \lambda_{1}/\lambda_{2} is proportional to

For proton and photon wavelength is given as - \displaystyle \lambda_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}=\frac{\mathrm{h}}{\sqrt{2\mathrm{m}\mathrm{E}}},\ \displaystyle \lambda_{\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}=\frac{\mathrm{h}\mathrm{c}}{\mathrm{E}} .So, the answer is option (B).

Q: A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3\times 10^{8}m/s . The final momentum of the object is:

Sol . (B) t=100\times 10^{-9} sec,\ P=30\times 10^{-3} Watt, C=3\times 10^{8}m/s Incident energy = Pt By debroglie wavelength, \lambda=h/p and Energy of photon is E=hc/\lambda From above two equations, E=pc Momentum p=\dfrac{Pt}{C}=\dfrac{30\times 10^{-3}\times 100\times 10^{-9}}{3\times 10^{8}}=1.0\times 10^{-17} kg ms ^{-1} So, the answer is option (B).

Q: The speed of the particle that can take discrete values is proportional to

As given in the questionLet the no. of loops in the wave be n Let wavelength be \lambda Debroglie wavelength \lambda = \cfrac{h}{mv} ------------(1)Also n \lambda = 2 \pi a --------------(2)Substituting above v = \cfrac{nh}{2am} v \propto n So, the answer is option (D).

Q: Light of wavelength \displaystyle { \lambda }_{ ph } falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is \displaystyle \phi and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is \displaystyle { \lambda }_{ e } , which of the following statement(s) is(are) true?

{ \lambda }_{ e }= minimum be broglie wavelength. \dfrac { hc }{ { \lambda }_{ ph } } =\dfrac { hc }{ { \lambda }_{ e } } +\phi +eV \Rightarrow hc(\dfrac { -1 }{ { \lambda }_{ ph }^{ 2 } } d{ \lambda }_{ ph })=hc(\dfrac { -1 }{ { \lambda }_{ e }^{ 2 } } d{ \lambda }_{ e }) \Rightarrow \dfrac { d{ \lambda }_{ ph } }{ d{ \lambda }_{ e } } =\dfrac { { \lambda }_{ ph }^{ 2 } }{ { \lambda }_{ e }^{ 2 } } This denies option A, B and C. V>>\dfrac { \phi }{ e } Energy of electron, E=\dfrac { { P }^{ 2 } }{ 2m } \lambda_e =\dfrac { h }{ p } =\dfrac { h }{ \sqrt { 2mE } } =\dfrac{h}{\sqrt{2meV}} This supports option D.

Question 1

The allowed energy for the particle for a particular value of n is proportional to :

Accepted Answer

a = \cfrac{n \lambda}{2} De broglie wavelength  \lambda = \cfrac{h}{mv} Subsitute  p =\cfrac{nh}{2a}  E = \cfrac{1}{2}mv^2= \cfrac{p^2}{2m} =\cfrac{n^2h^2}{8a^2m}

Question 2

A photoelectric material having work-function $ϕ_{0}$ is illuminated with light of wavelength $λ$ $(λ < \frac{h c}{ϕ _{0}})$ . The fastest photoelectron has a de Broglie wavelength $λ_{d}$ . A change in wavelength of the incident light by $Δ λ$ results in a change $Δ λ_{d}$ in $λ_{d}$ . Then the ratio $Δ λ_{d} / Δ λ$ is proportional to

Accepted Answer

According to photoelectric equation,    \dfrac{hc}{\lambda} - \phi =\dfrac{1}{2}mv^2=\dfrac{p^2}{2m}=\dfrac{h^2}{2m\lambda_d^2} \dfrac{-hc}{\lambda^2}	imes \Delta \lambda = \dfrac{-h^2}{m\lambda_d^3}	imes \Delta \lambda_d  \dfrac{\Delta \lambda_d}{\Delta \lambda} \propto \dfrac{ \lambda_d^3}{\lambda^2}

Question 3

A proton has kinetic energy  \mathrm{E}=100\mathrm{k}\mathrm{e}\mathrm{V}  which is equal to that of a photon. The wavelength of photon is  \lambda_{2}  and that of proton is  \lambda_{1} . The ratio of  \lambda_{1}/\lambda_{2}  is proportional to

Accepted Answer

For proton and photon wavelength is given as - \displaystyle \lambda_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}=\frac{\mathrm{h}}{\sqrt{2\mathrm{m}\mathrm{E}}},\ \displaystyle \lambda_{\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}=\frac{\mathrm{h}\mathrm{c}}{\mathrm{E}} .So, the answer is option (B).

Question 4

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 $m W$ and the speed of light is $3 \times 1 0^{8} m / s$ . The final momentum of the object is:

Accepted Answer

Sol . (B) t=100	imes 10^{-9} sec,\ P=30	imes 10^{-3} Watt,  C=3	imes 10^{8}m/s Incident energy  = Pt By debroglie wavelength,  \lambda=h/p and Energy of photon is  E=hc/\lambda From above two equations,  E=pc  Momentum  p=\dfrac{Pt}{C}=\dfrac{30	imes 10^{-3}	imes 100	imes 10^{-9}}{3	imes 10^{8}}=1.0	imes 10^{-17}  kg ms ^{-1}  So, the answer is option (B).

Question 5

The speed of the particle that can take discrete values is proportional to

Accepted Answer

As given in the questionLet the no. of loops in the wave be   n Let wavelength be  \lambda  Debroglie wavelength  \lambda = \cfrac{h}{mv}  ------------(1)Also  n \lambda = 2 \pi a   --------------(2)Substituting above  v = \cfrac{nh}{2am} v \propto n So, the answer is option (D).

Question 6

Light of wavelength  \displaystyle { \lambda  }_{ ph }  falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is  \displaystyle \phi   and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is  \displaystyle { \lambda  }_{ e } , which of the following statement(s) is(are) true?

Accepted Answer

{ \lambda  }_{ e }=  minimum be broglie wavelength. \dfrac { hc }{ { \lambda  }_{ ph } } =\dfrac { hc }{ { \lambda  }_{ e } } +\phi +eV \Rightarrow   hc(\dfrac { -1 }{ { \lambda  }_{ ph }^{ 2 } } d{ \lambda  }_{ ph })=hc(\dfrac { -1 }{ { \lambda  }_{ e }^{ 2 } } d{ \lambda  }_{ e }) \Rightarrow   \dfrac { d{ \lambda  }_{ ph } }{ d{ \lambda  }_{ e } } =\dfrac { { \lambda  }_{ ph }^{ 2 } }{ { \lambda  }_{ e }^{ 2 } }  This denies option A, B and C. V>>\dfrac { \phi  }{ e }  Energy of electron, E=\dfrac { { P }^{ 2 } }{ 2m }  \lambda_e =\dfrac { h }{ p } =\dfrac { h }{ \sqrt { 2mE }  }  =\dfrac{h}{\sqrt{2meV}} This supports option D.

Dual Nature Of Radiation And Matter

Physics
493 Views

The allowed energy for the particle for a particular value of n is proportional to :

A proton has kinetic energy $E = 100 k e V$ which is equal to that of a photon. The wavelength of photon is $λ_{2}$ and that of proton is $λ_{1}$ . The ratio of $λ_{1} / λ_{2}$ is proportional to

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 $m W$ and the speed of light is $3 \times 1 0^{8} m / s$ . The final momentum of the object is:

The speed of the particle that can take discrete values is proportional to

Dual Nature Of Radiation And Matter

Physics 493 Views

The allowed energy for the particle for a particular value of n is proportional to :

A proton has kinetic energy E=100keV which is equal to that of a photon. The wavelength of photon is λ2​ and that of proton is λ1​. The ratio of λ1​/λ2​ is proportional to

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30mWand the speed of light is 3×108m/s. The final momentum of the object is:

The speed of the particle that can take discrete values is proportional to

Physics
493 Views

A proton has kinetic energy $E = 100 k e V$ which is equal to that of a photon. The wavelength of photon is $λ_{2}$ and that of proton is $λ_{1}$ . The ratio of $λ_{1} / λ_{2}$ is proportional to

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 $m W$ and the speed of light is $3 \times 1 0^{8} m / s$ . The final momentum of the object is: