Photons of energy E are incident on two different photosensitive surfaces X and Y. The work functions of the surfaces are _X and _Y respectively, where _X < _Y < E . If _X and _Y are the minimum de Broglie wavelengths of the emitted photoelectrons from surfaces X and Y respectively, which of the following statements is correct regarding their relationship initially, and the effect on the ratio _X/ _Y if the incident

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy of emitted photoelectrons is K = E - . Since _X K_Y . The minimum de Broglie wavelength of the photoelectrons is given by = h 2mK . Because K_X > K_Y , we have _X The ratio of the wavelengths is _X _Y = K_Y K_X = E - _Y E - _X . When the incident energy E is doubled to 2E , the new ratio becomes 2E - _Y 2E - _X . For any positive fraction where the numerator is less than the denominator, adding the same positive amount to both (or scaling E