Modern Physics Formula for NEET 2027 Exam

Modern Physics formula sheet for NEET 2027: Chapter-wise

This formula sheet provides the most important NEET Modern Physics formulas for the chapters Dual Nature of Matter and Radiation, Atoms and Nuclei, and Electronic Devices. The formulas are easy to remember, chapter-wise, and cover most scoring concepts required for NEET. This comprehensive list of Modern Physics equations for NEET helps students quickly revise, practice important concepts, and improve their preparation efficiently. It is an effective tool for last-minute revision and concept reinforcement in Modern Physics.

Dual Nature of Matter and Radiation

The formulas with equations are given below:

1. This formula helps to find the wavelength of a moving particle using its mass and velocity:

$\lambda = \frac{h}{p} = \frac{h}{mv}$

Example: If $v = 10^6$ m/s and $m = 9.1 \times 10^{-31}$ kg, then

$\lambda = \frac{6.63 \times 10^{-34}}{9.1 \times 10^{-31} \times 10^6} = 7.29 \times 10^{-10}$ m

2. This is the formula to calculate kinetic energy using wavelength:

$KE = \frac{h^2}{2m\lambda^2}$

Example: For $\lambda = 1 \times 10^{-10}$ m,

$KE = \frac{(6.63 \times 10^{-34})^2}{2 \times 9.1 \times 10^{-31} \times (1 \times 10^{-10})^2} \approx 2.4 \times 10^{-17}$ J

3. This is Einstein's photoelectric equation showing the energy of the incident light:

$h\nu = \phi + \frac{1}{2}mv_{\max}^2$

Example: If $\phi = 2$ eV and $h\nu = 3$ eV,

$\frac{1}{2}mv_{\max}^2 = 3 - 2 = 1$ eV

4. This gives the relation between threshold frequency and work function:

$\phi = h\nu_0$

Example: If $\nu_0 = 5 \times 10^{14}$ Hz,

$\phi = 6.63 \times 10^{-34} \times 5 \times 10^{14} = 3.315 \times 10^{-19}$ J

5. This relates stopping potential and maximum kinetic energy:

$eV_0 = \frac{1}{2}mv_{\max}^2$

Example: If $v_{\max} = 10^6$ m/s, then

$V_0 = \frac{9.1 \times 10^{-31} \times (10^6)^2}{2 \times 1.6 \times 10^{-19}} \approx 2.84$ V

6. This formula links frequency with wavelength and the speed of light:

$\nu = \frac{c}{\lambda}$

Example: For $\lambda = 500$ nm,

$\nu = \frac{3 \times 10^8}{500 \times 10^{-9}} = 6 \times 10^{14}$ Hz

7. This calculates the threshold frequency from the work function:

$\nu_0 = \frac{\phi}{h}$

Example: If $\phi = 2$ eV,

$\nu_0 = \frac{2 \times 1.6 \times 10^{-19}}{6.63 \times 10^{-34}} \approx 4.83 \times 10^{14}$ Hz

8. This formula calculates the wavelength of an electron accelerated through a potential difference:

$\lambda = \frac{h}{\sqrt{2meV}}$

Example: For $V = 100$ V,

$\lambda = \frac{6.63 \times 10^{-34}}{\sqrt{2 \times 9.1 \times 10^{-31} \times 1.6 \times 10^{-19} \times 100}} \approx 1.23 \times 10^{-10}$ m

Atoms and Nuclei

This gives the radius of an atom’s orbit in Bohr’s model:

$r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2 Z} = 0.53 \cdot \frac{n^2}{Z}$

Example: For hydrogen in the 1st orbit ($n = 1$),

$r = 0.53$ Å

This gives the energy of an electron in the $n$th orbit:

$E_n = -\frac{13.6Z^2}{n^2}$

Example: For $Z = 1$, $n = 2$,

$E = -\frac{13.6}{4} = -3.4$ eV

This gives the speed of an electron in the $n$th orbit:

$v_n = \frac{Ze^2}{2\epsilon_0 h} \cdot \frac{1}{n}$

Example: In hydrogen ($Z = 1$, $n = 1$),

$v = 2.18 \times 10^6$ m/s

This gives the wavelength of radiation emitted or absorbed:

$\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$

Example: For $n_2 = 3$, $n_1 = 2$, $Z = 1$,

$\frac{1}{\lambda} = 1.097 \times 10^7\left(\frac{1}{4} - \frac{1}{9}\right) = 1.523 \times 10^6$ m$^{-1}$

This is the formula for binding energy using mass defect:

$BE = \Delta m \cdot c^2$

Example: If $\Delta m = 0.0025$ u,

$BE = 0.0025 \times 931 = 2.33$ MeV

This formula calculates the mass defect of a nucleus:

$\Delta m = Zm_p + (A-Z)m_n - M_{\text{nucleus}}$

Example: For He-4,

$\Delta m = 2(1.00728) + 2(1.00867) - 4.00260 = 0.0304$ u

This shows how the number of nuclei decays with time:

$N = N_0 e^{-\lambda t}$

Example: If $\lambda = 0.693$ and $t = 1$,

$N = N_0 e^{-0.693} = \frac{N_0}{2}$

This formula gives the decay constant from the half-life:

$\lambda = \frac{0.693}{T_{1/2}}$

Example: For $T_{1/2} = 10$ days,

$\lambda = \frac{0.693}{10} = 0.0693$ day$^{-1}$

This gives the activity of a radioactive sample:

$A = \lambda N$

Example: If $\lambda = 0.1$ and $N = 500$,

$A = 0.1 \times 500 = 50$ decays/s

Electronic Devices

1. This gives the current gain in a transistor:

$\beta = \frac{\Delta I_C}{\Delta I_B}$

Example: If $I_C = 3$ mA and $I_B = 30,\mu$A,

$\beta = \frac{3}{0.03} = 100$

2. This is the ratio of collector current to emitter current:

$\alpha = \frac{\Delta I_C}{\Delta I_E}$

Example: If $I_C = 9$ mA and $I_E = 10$ mA,

$\alpha = \frac{9}{10} = 0.9$

3. These give the relation between $\alpha$ and $\beta$ in a transistor:

$\beta = \frac{\alpha}{1-\alpha}, \quad \alpha = \frac{\beta}{1+\beta}$

Example: If $\alpha = 0.98$, then

$\beta = \frac{0.98}{1-0.98} = \frac{0.98}{0.02} = 49$

4. This gives the average current in a full-wave rectifier:

$I_{\text{avg}} = \frac{2I_0}{\pi}$

Example: If $I_0 = 10$ A,

$I_{\text{avg}} = \frac{20}{\pi} \approx 6.37$ A

5. This gives the average current in a half-wave rectifier:

$I_{\text{avg}} = \frac{I_0}{\pi}$

Example: If $I_0 = 10$ A,

$I_{\text{avg}} = \frac{10}{\pi} \approx 3.18$ A

6. These are the maximum efficiency values of rectifiers:

$\eta_{\text{full wave}} = 81.2%$

$\eta_{\text{half wave}} = 40.6%$

7. This shows that a Zener diode maintains a constant voltage in the breakdown region:

$V_Z = \text{constant}$

Example: If the Zener breakdown voltage is $5.6$ V, the output remains approximately $5.6$ V even if the input voltage rises, provided the diode operates within its specified breakdown range.

8. This is the logic gate formula for an AND gate:

$Y = A \cdot B$

Example: If $A = 1$ and $B = 1$,

$Y = 1$

9. The OR gate gives a high output ($1$) if at least one of the inputs is high:

$Y = A + B$

Example: If $A = 1$ and $B = 0$,

$Y = 1$

10. The NOT gate gives the inverse or complement of the input:

$Y = \overline{A}$

Example: If $A = 0$,

$Y = 1$

11. The NAND gate gives a low output ($0$) only when all inputs are high:

$Y = \overline{A \cdot B}$

Example: If $A = 1$ and $B = 1$,

$Y = 0$

12. The NOR gate gives a high output ($1$) only when all inputs are low:

$Y = \overline{A + B}$

Example: If $A = 0$ and $B = 0$,

$Y = 1$

These formulas of Modern Physics for NEET have to be understood so that the students can do well in the exam. With practice and study, students can apply these formulas to solve Modern Physics questions without any difficulty. A smart revision strategy and practice of these equations from time to time will help the students have a clear idea about Modern Physics and perform well in preparation for the NEET 2027 exam.

Importance of Modern Physics in NEET 2027

Modern physics talks about new concepts in physics that came after Newton’s time. It mainly deals with two big discoveries: relativity and quantum mechanics. These ideas help us understand things like the photoelectric effect, how atoms work (Bohr’s model), nuclear physics, and radioactivity.

Learning the important Modern Physics formulas for NEET 2027 is effective, as many questions are directly based on these formulas, and knowing them helps you solve problems quickly in the NEET exam.

Students who are wondering how to study Physics for NEET have to focus on Modern Physics topics for NEET, like the photoelectric effect, Rutherford's model of the atom, radioactivity, wave nature of matter, etc., as they are highly scoring and require less attention and practice, while preparing.

Chapter‑Wise Weightage of Modern Physics (2021-2026 Analysis)

The modern physics chapters for NEET focus on topics that came after Newton’s time and are important for the exam. These topics are formula‑driven, high‑yield, and together contribute 6-8 direct questions every year. The modern physics chapter-wise weightage analysis is given below: