Image. Electromagnetic radiation of wavelength 1242 Å falls on a metal of work function 2 eV. The target is connected to a 5 V cell as shown. The emitted electrons pass through a hole into hydrogen gas in the ground state. Find the number of spectral lines emitted when the excited H atoms return to ground. Take hc = 12420 eV·Å.
Physics · Atomic Structure and X-rays
JEE Mains Advanced

Question

Image. Electromagnetic radiation of wavelength 1242 Å falls on a metal of work function 2 eV. The target is connected to a 5 V cell as shown. The emitted electrons pass through a hole into hydrogen gas in the ground state. Find the number of spectral lines emitted when the excited H atoms return to ground. Take hc = 12420 eV·Å.

Physics · Atomic Structure and X-rays

G1 Physics · Accepted Answer

Step 1: Photon energy is 12420/1242 = 10 eV; after subtracting the 2 eV work function and adding the 5 eV accelerating energy, electrons can provide up to 13 eV to H atoms. This can excite hydrogen up to n=4, producing 4×3/2 = 6 possible emission lines.