In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of $3.15 \times 10^{-18} J$ from the radiations of $600 \mathrm{~nm}$, calculate the number of photons received by the detector.

Home » In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of from the radiations of , calculate the number of photons received by the detector.

In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of $3.15 \times 10^{-18} J$ from the radiations of $600 \mathrm{~nm}$ , calculate the number of photons received by the detector.

CBSE | Chemistry | Class 11 | NCERT | Structure of Atom

In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of $3.15 \times 10^{-18} J$ from the radiations of $600 \mathrm{~nm}$ , calculate the number of photons received by the detector.

From the expression of energy of one photon (E),
$E=\frac{h c}{\lambda}$
Where,
$\lambda$ denotes the wavelength of the radiation
$\mathrm{h}$ is Planck’s constant
c denotes the velocity of the radiation
Substituting these values in the expression for $E$ :
$E=\frac{\left(6.626 \times 10^{-34} J s\right)\left(3 \times 10^{8} \mathrm{~ms}^{-1}\right)}{\left(600 \times 10^{-9}\right)}=3.313 \times 10^{-19} \mathrm{~J}$
Energy held by one photon $=3.313 \times 10^{-19} J$
No. photons received with $3.15 \times 10^{-18} J$ energy
$=\frac{3.15 \times 10^{-18} J}{3.313 \times 10^{-19} J}$
$=9.5$
$\approx 10$