Solving Photoelectric Effect Numericals in eV

Physics · Dual Nature Of Radiation And Matter · NEET

To solve photoelectric numericals fast, work in electron-volts (eV) and nanometres (nm). Find photon energy with E(eV) = 1240 / lambda(nm), then use Einstein's equation KEmax = E - W (work function). Since eV0 = KEmax, the stopping potential V0 (in volts) equals KEmax (in eV) numerically. Memory hook: "1240 unlocks the door, subtract the work, read the volt."
Solving in eV: three quick stepsStep 1: Photon energyE = 1240 / lambda(nm)answer in eVStep 2: Max KEKEmax = E - WW = work function (eV)Step 3: Stopping VV0 = KEmaxvolts = eV numberWorked example: lambda = 400 nm, W = 2.0 eVE = 1240/400 = 3.1 eV -> KEmax = 3.1 - 2.0 = 1.1 eV -> V0 = 1.1 V
The three-step eV method: convert wavelength to photon energy with 1240/lambda, subtract the work function to get KEmax, and read the stopping potential directly in volts.

Your doubts, answered

Why do we use the number 1240 in these numericals?

1240 is a ready-made shortcut for h times c. When you put Planck's constant h = 6.63e-34 J s, speed of light c = 3e8 m/s, and divide by the electron charge 1.6e-19 C, the product hc comes out close to 1240 eV nm. So E(eV) = 1240 / lambda(nm) gives photon energy directly in eV when wavelength is in nanometres. This saves you from writing out powers of ten each time.

How do I convert a wavelength to energy in eV?

First make sure the wavelength is in nanometres (nm). If it is given in angstrom, divide by 10 (1 nm = 10 angstrom). If it is in metres, multiply by 1e9. Then apply E(eV) = 1240 / lambda(nm). Example: light of 620 nm has E = 1240 / 620 = 2 eV. That is the whole photon energy in one step.

How do I find the stopping potential in eV problems?

Stopping potential V0 comes from eV0 = KEmax, and KEmax = E - W. Because e (the charge) appears on both sides when energies are in eV, the number for V0 in volts is the same as KEmax in eV. So if KEmax = 1.2 eV, then V0 = 1.2 V. No extra conversion is needed. This is the biggest time-saver in the chapter.

When do I actually have to convert eV to joules?

Convert to joules only when the answer must be in SI units, such as finding photocurrent, number of photons per second, or momentum in kg m/s. For pure comparison questions (does emission happen, which metal emits, what is V0) stay fully in eV. Rule: 1 eV = 1.6e-19 J. Multiply eV by 1.6e-19 to get joules.

How do I get the work function if the stopping potential is given?

Rearrange Einstein's equation: W = E - eV0. Work in eV throughout. Example: light of 400 nm gives E = 1240/400 = 3.1 eV. If V0 = 1.1 V, then eV0 = 1.1 eV, so W = 3.1 - 1.1 = 2.0 eV. The work function of the metal is 2.0 eV.

What if photon energy is less than the work function?

Then KEmax = E - W would be negative, which is impossible. It means no photoelectrons are emitted at all, so KEmax = 0, current = 0, and stopping potential = 0. Always check E versus W first. Emission happens only when photon energy E is greater than or equal to the work function W.

⚠️ The NEET trap
Reading the stopping potential straight off as KEmax in joules, or forgetting that lambda must be in nm before using 1240.
eV0 = KEmax means V0 in volts equals KEmax in eV numerically (not in joules). And E(eV) = 1240 / lambda(nm) only works when wavelength is in nanometres.
🧠 NTA loves giving wavelength in angstrom (e.g. 4000 A). Convert to 400 nm first, then use 1240. Skipping this gives an answer off by a factor of 10.

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Frequently asked

What is the fastest formula to solve photoelectric numericals in eV?

Use E(eV) = 1240 / lambda(nm) for photon energy, then KEmax = E - W, and V0(volts) = KEmax(eV). These three steps solve almost every eV numerical in the chapter.

Is 1240 exact or approximate?

It is a rounded value of hc expressed in eV nm. The exact figure is about 1239.8 eV nm, but 1240 is accurate enough for NEET and keeps the arithmetic simple.

Can I use 12400 with angstrom instead?

Yes. E(eV) = 12400 / lambda(angstrom) is the same shortcut for wavelength in angstrom. Pick one system and stay consistent so you do not mix nm and angstrom.

Do intensity or number of photons change the energy per photon?

No. Photon energy depends only on frequency or wavelength, so E = 1240/lambda is unchanged by intensity. Intensity changes only the number of photons, which affects current, not KEmax or stopping potential.

How do I find KEmax in joules if the question asks for it?

First find KEmax in eV using KEmax = E - W, then multiply by 1.6e-19. For example, KEmax = 1.5 eV = 1.5 times 1.6e-19 = 2.4e-19 J.