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Physics Question 19 – NEET-UG 2026

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A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron pe to that of photon pPh, pepPh is : (Take speed of light =3×108 ms−1, charge of electron =−1.6×10−19 C and mass of electron =9×10−31 kg)

The relationship between energy and momentum is different for a photon (massless particle) and an electron (particle with rest mass).

🥷
Ninja Strategy•Magnitude Estimation

Estimate the order of magnitude of the electron's and photon's momenta to quickly eliminate options that are too small (less than 1).

Step 1: Calculate the momentum of the photon (pPh)✦ Active

The energy of the photon is given as EPh=20 eV. First, convert this energy to Joules:

EPh=20 eV×(1.6×10−19 J/eV)=3.2×10−18 J

For a photon, the momentum is related to its energy by pPh=EPhc, where c is the speed of light (3×108 m/s). Therefore:

pPh=3.2×10−18 J3×108 m/s=3.23×10−26 kg m/s
Step 2: Calculate the momentum of the electron (pe)○ Expand

The energy of the electron is Ee=20 eV, which is 3.2×10−18 J. The rest mass energy of an electron is mec2≈0.51 MeV, which is much greater than 20 eV. Thus, the electron is non-relativistic. For a non-relativistic particle, the kinetic energy Ee and momentum pe are related by Ee=pe22me, which implies pe=2meEe. Given me=9×10−31 kg:

pe=2×(9×10−31 kg)×(3.2×10−18 J)

Simplify the expression:

pe=57.6×10−49=576×10−50=24×10−25 kg m/s
💡 Teacher's Secret Hint

Always check if the particle is relativistic or non-relativistic based on its kinetic energy compared to its rest mass energy.

Step 3: Calculate the ratio pepPh○ Expand

Now, calculate the ratio of the electron's momentum to the photon's momentum:

pepPh=24×10−25 kg m/s3.23×10−26 kg m/s

Simplify the ratio:

pepPh=24×10−25×33.2×10−26=72×10−253.2×10−26=723.2×10(−25−(−26))=723.2×101
pepPh=7203.2=720032=225

The ratio is 225.

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