Question

The threshold frequency for photoelectric emission of electrons from platinum is $1.3 \times {10^{15}}{s^{ - 1}}$. Then incorrect statement is:
A) The number of electrons ejected from the metal surface will depend upon the intensity.
B) The radiation having energy $1 \times {10^{ - 20}}J$ will be able to cause photoelectric effect.
C) If radiation having frequency $1.3 \times {10^{14}}{s^{ - 1}}$ strikes the platinum surface, photo electrons will not be ejected.
D) The kinetic energy of the emitted electrons will increase with increase in frequency provided it is greater than $1.3 \times {10^{15}}{s^{ - 1}}$.

Answer 1

Threshold frequency is the minimum frequency required for photoelectric emission. The formula of photon energy is $E = hv$. By putting the values in this formula we get our required answer.

Complete step by step answer:
Threshold frequency is defined as the minimum frequency of incident radiation below which the photoelectric emission is not possible completely irrespective of the intensity of incident radiation. The solution is calculated as follows:
Energy required for photoelectric emission = $hv$
Here, $v$ is the threshold frequency and $h$ is the Plank’s Constant with value $6.6 \times {10^{ - 34}}Js$ . Now, we are given with value of $v$ which is,
$v = 1.3 \times {10^{15}}/\sec$
Now, finding the energy required for emission we will multiply frequency with the Plank’s constant.
$\Rightarrow 6.6 \times {10^{ - 34}} \times 1.3 \times {10^{15}}$
$\Rightarrow 8.58 \times {10^{ - 19}}J$
Now, we got threshold energy as $8.58 \times {10^{ - 19}}J$ .
Now, according to the options, the first option is correct as electron ejection depends on the intensity of threshold energy. The second option is incorrect as $1 \times {10^{ - 20}}J$ will not be able to eject electrons as the energy is less than the threshold energy. The third option is correct as the value in the option is less than threshold value and therefore electrons will not eject. According to the fourth option kinetic energy will increase with frequency which is also true as energy is directly proportional to frequency.

Therefore, the data in option A, C and D are correct and data in option B is incorrect. Thus the correct answer is option B.

Additional Information: The photoelectric effect is the emission of electrons when electromagnetic radiation such as light hits a material. Electrons emitted in this manner are called photoelectrons. It is used in electronic devices specialized for light detection and precisely timed electron emission. In classical electromagnetic theory, the photoelectric effect was attributed to the transfer of energy from the continuous light waves to an electron.

Note: Threshold energy is an important part of particle physics. It is the minimum kinetic energy required when a pair of travelling particles must have when they collide. It is always greater than or equal to rest energy of the desired particle.