There are two sources of light, each emitting with a power of $100 \,W.$ One emits $X-$ rays of wavelength $1\, nm$ and the other visible light at $500\, nm$. Find the ratio of number of photons of $X-$ rays to the photons of visible light of the given wavelength ?
There are two sources of light, each emitting with a power of $100 \,W.$ One emits $X-$ rays of wavelength $1\, nm$ and the other visible light at $500\, nm$. Find the ratio of number of photons of $X-$ rays to the photons of visible light of the given wavelength ?
Power of radiation,
$\mathrm{P}=\frac{\mathrm{E}_{n}}{t}=\frac{n h f}{t}=\frac{n h c}{t \lambda}$
$\therefore \mathrm{P}=n^{\prime} \frac{h c}{\lambda} \quad$ (Where $n^{\prime}=$ no. of photons emitted per unit time)
$\therefore n^{\prime}=\left(\frac{\mathrm{P}}{h c}\right) \lambda$ $\therefore n^{\prime} \propto \lambda \quad(\because$ Here P, $h, c$ are constant $)$ $\therefore \frac{n_{1}^{\prime}}{n_{2}^{\prime}}=\frac{\lambda_{1}}{\lambda_{2}}$ $=\frac{1 \mathrm{~nm}}{500 \mathrm{~nm}}$ $\therefore \frac{n_{1}^{\prime}}{n_{2}^{\prime}}=\frac{1}{500}$
$\therefore\frac{n_{1}^{\prime}}{n_{2}^{\prime}}=\frac{\lambda_{1}}{\lambda_{2}}$
$=\frac{1 \mathrm{~nm}}{500 \mathrm{~nm}}$
$\therefore \frac{n_{1}^{\prime}}{n_{2}^{\prime}}=\frac{1}{500}$
Similar Questions
Assertion : Photoelectric saturation current increases with the increase in frequency of incident light.
Reason : Energy of incident photons increases with increase in frequency and as a result photoelectric current increases.
Assertion : Photoelectric saturation current increases with the increase in frequency of incident light.
Reason : Energy of incident photons increases with increase in frequency and as a result photoelectric current increases.
- [AIIMS 2015]
If the energy of a photon corresponding to a wavelength of $6000 \mathring A$ is $3.32 \times {10^{ - 19}}J$, the photon energy for a wavelength of $4000 \mathring A$ will be ............ $eV$
If $c$ is the velocity of light in free space, the correct statements about photon among the following are:
$A$. The energy of a photon is $E=h v$.
$B$. The velocity of a photon is $c$.
$C$. The momentum of a photon, $p=\frac{h v}{c}$.
$D$. In a photon-electron collision, both total energy and total momentum are conserved.
$E$. Photon possesses positive charge.
Choose the correct answer from the options given below:
If $c$ is the velocity of light in free space, the correct statements about photon among the following are:
$A$. The energy of a photon is $E=h v$.
$B$. The velocity of a photon is $c$.
$C$. The momentum of a photon, $p=\frac{h v}{c}$.
$D$. In a photon-electron collision, both total energy and total momentum are conserved.
$E$. Photon possesses positive charge.
Choose the correct answer from the options given below:
- [NEET 2024]
There are ${n_1}$ photons of frequency ${\gamma _1}$ in a beam of light. In an equally energetic beam, there are ${n_2}$ photons of frequency ${\gamma _2}$. Then the correct relation is
There are ${n_1}$ photons of frequency ${\gamma _1}$ in a beam of light. In an equally energetic beam, there are ${n_2}$ photons of frequency ${\gamma _2}$. Then the correct relation is
In a photo cell, the photo-electrons emission takes place
In a photo cell, the photo-electrons emission takes place