A perfectly reflecting mirror of mass M mount | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The momentum of one photon is $p = \frac{h}{\lambda}$.When $N$ photons strike the mirror,the total momentum transferred to the mirror is $\Delta P

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) The momentum of one photon is $p = \frac{h}{\lambda}$.When $N$ photons strike the mirror,the total momentum transferred to the mirror is $\Delta P = 2Np = \frac{2Nh}{\lambda}$.By the conservation of linear momentum,this impulse imparts an initial velocity $v$ to the mirror of mass $M$ at the equilibrium position:$Mv = \frac{2Nh}{\lambda} \implies v = \frac{2Nh}{M\lambda}$.For a spring-mass system,the maximum displacement (amplitude $A$) is related to the velocity at the mean position by $v = A\Omega$.Given $A = 1 \mu	ext{m} = 10^{-6} 	ext{ m}$,we have:$A\Omega = \frac{2Nh}{M\lambda} \implies N = \frac{M\Omega A \lambda}{2h}$.Rearranging the given expression $\frac{4 \pi M \Omega}{h} = 10^{24} 	ext{ m}^{-2}$,we get $\frac{M\Omega}{h} = \frac{10^{24}}{4\pi} 	ext{ m}^{-2}$.Substituting the values:$N = \left( \frac{10^{24}}{4\pi} ight) 	imes \frac{A \lambda}{2} = \frac{10^{24}}{4\pi} 	imes \frac{10^{-6} 	imes 8\pi 	imes 10^{-6}}{2}$.$N = \frac{10^{24} 	imes 8\pi 	imes 10^{-12}}{8\pi} = 10^{12}$.Since $N = x 	imes 10^{12}$,we find $x = 1$.

Similar Questions

The number of photons per second on an average emitted by a source of monochromatic light of wavelength $600 \, nm$,when it delivers a power of $3.3 \times 10^{-3} \, W$,is: $(h = 6.6 \times 10^{-34} \, Js)$

The number of photons emitted per second from a $60 \ W$ light bulb is .......... . The wavelength of the photon is $660 \ nm$. $(h = 6.6 \times 10^{-34} \ J \cdot s)$

The energy of a quantum of frequency $10^{15} \ Hz$ and $h = 6.6 \times 10^{-34} \ J \cdot s$ will be:

If $h$ is Planck's constant in $SI$ system,the momentum of a photon of wavelength $0.01 \, \mathring{A}$ is:

$A$ photon of wavelength $4400 \ \mathring A$ passes through a vacuum. Its effective mass and momentum are,respectively,............

Vedclass Test Series

Exam Paper Generator

Online Exam Module