In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy $10.2\; BeV$ into two $\gamma$ -rays of equal energy. What is the wavelength associated with each $\gamma$ -ray? $\left(1\; BeV =10^{9}\; eV \right)$
In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy $10.2\; BeV$ into two $\gamma$ -rays of equal energy. What is the wavelength associated with each $\gamma$ -ray? $\left(1\; BeV =10^{9}\; eV \right)$
Total energy of two $\gamma$ -rays: $E =10.2 \,BeV$
$=10.2 \times 10^{9} eV$
$=10.2 \times 10^{9} \times 1.6 \times 10^{-10}\, J$
Hence, the energy of each $\gamma$ -ray
$E^{\prime}=\frac{E}{2}$
$=\frac{10.2 \times 1.6 \times 10^{-10}}{2}=8.16 \times 10^{-10}\, J$
Plank's constant, $h=6.626 \times 10^{-34}\, Js$
Speed of light $c=3 \times 10^{8} \,m / s$
Energy is related to wavelength as:
$E^{\prime}=\frac{h c}{\lambda}$
$\lambda=\frac{h c}{E^{\prime}}$
$=\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{8.16 \times 10^{-10}}=2.436 \times 10^{-16} \,m$
Therefore, the wavelength associated with each $\gamma$ -ray is $2.436 \times 10^{-16}\; \,m$
Similar Questions
The minimum intensity of light to be detected by human eye is ${10^{ - 10}}W/{m^2}$. The number of photons of wavelength $5.6 \times {10^{ - 7}}m$ entering the eye, with pupil area ${10^{ - 6}}{m^2}$, per second for vision will be nearly
The minimum intensity of light to be detected by human eye is ${10^{ - 10}}W/{m^2}$. The number of photons of wavelength $5.6 \times {10^{ - 7}}m$ entering the eye, with pupil area ${10^{ - 6}}{m^2}$, per second for vision will be nearly
The momentum of a photon of energy $h\nu $ will be
The momentum of a photon of energy $h\nu $ will be
An astronaut floating freely in space decides to use his flash light as a rocket. He shines a $10$ watt light beam in a fixed direction so that he acquires momentum in the opposite direction. If his mass is $80$ kg, how long must he need to reach a velocity of $1$ $ms^{-1}$
An astronaut floating freely in space decides to use his flash light as a rocket. He shines a $10$ watt light beam in a fixed direction so that he acquires momentum in the opposite direction. If his mass is $80$ kg, how long must he need to reach a velocity of $1$ $ms^{-1}$
The energy of a photon of light of wavelength $450 nm$ is
The energy of a photon of light of wavelength $450 nm$ is
One day on a spacecraft corresponds to $2$ days on the earth. The speed of the spacecraft relative to the earth is
One day on a spacecraft corresponds to $2$ days on the earth. The speed of the spacecraft relative to the earth is