Select the correct statement regarding photoelectric effect

Here are the solutions to the questions. 61. Select the correct statement regarding photoelectric effect Step 1: Analyze the options based on the principles of the photoelectric effect. • The number of ejected electrons (photocurrent) is directly proportional to the intensity of the incident light. • The kinetic energy of the ejected electrons depends on the frequency of the incident light and the work function of the material, not the intensity. • For the photoelectric effect to occur, the frequency of the incident light must be above a certain threshold frequency. Step 2: Evaluate each statement. (1) "Number of ejected electrons are independent of intensity of light" - This is incorrect. The number of ejected electrons increases with light intensity. (2) "Kinetic energy of electrons are independent of intensity of light" - This is correct. The kinetic energy of photoelectrons depends on the frequency of light, not its intensity. (3) "Kinetic energy of electrons are independent of frequency of light" - This is incorrect. The kinetic energy of photoelectrons is directly proportional to the frequency of light above the threshold frequency. (4) "Number of ejected electrons depends on the frequency of light" - This is incorrect. The number of ejected electrons depends on the intensity of light. The correct statement is (2). The final answer is 2 62. The frequency of light emitted for the transition of n = 9 to n = 3 of Li^2+ is equal to transition in H-atom corresponding to which of the two following transition? Step 1: Write the formula for the frequency of emitted light for a hydrogen-like atom. The frequency of light emitted during a transition from an initial state n_2 to a final state n_1 in a hydrogen-like atom with atomic number Z is given by: = (R_H Z^2)/(h) ( (1)/(n_1^2) - (1)/(n_2^2) ) where R_H is the Rydberg constant and h is Planck's constant. Step 2: Calculate the term ( (1)/(n_1^2) - (1)/(n_2^2) ) for the Li^2+ transition. For Li^2+, Z=3. The transition is from n_2=9 to n_1=3. _Li^2+ = (R_H (3)^2)/(h) ( (1)/(3^2) - (1)/(9^2) ) _Li^2+ = (9 R_H)/(h) ( (1)/(9) - (1)/(81) ) _Li^2+ = (9 R_H)/(h) ( (9)/(81) - (1)/(81) ) _Li^2+ = (9 R_H)/(h) ( (8)/(81) ) _Li^2+ = (R_H)/(h) ( (8)/(9) ) Step 3: Find the equivalent transition for a Hydrogen atom. For a Hydrogen atom, Z=1. We need to find a transition (n_2 to n_1) such that its frequency _H is equal to _Li^2+. _H = (R_H (1)^2)/(h) ( (1)/(n_1^2) - (1)/(n_2^2) ) Equating the frequencies: (R_H)/(h) ( (1)/(n_1^2) - (1)/(n_2^2) ) = (R_H)/(h) ( (8)/(9) ) So, we need to find an option where: (1)/(n_1^2) - (1)/(n_2^2) = (8)/(9) Step 4: Check the given options for the H-atom transition. (1) n_2 = 5 to n_1 = 1: (1)/(1^2) - (1)/(5^2) = 1 - (1)/(25) = (25-1)/(25) = (24)/(25) (2) n_2 = 3 to n_1 = 2: (1)/(2^2) - (1)/(3^2) = (1)/(4) - (1)/(9) = (9-4)/(36) = (5)/(36) (3) n_2 = 3 to n_1 = 1: (1)/(1^2) - (1)/(3^2) = 1 - (1)/(9) = (9-1)/(9) = (8)/(9) (4) n_2 = 6 to n_1 = 2: (1)/(2^2) - (1)/(6^2) = (1)/(4) - (1)/(36) = (9)/(36) - (1)/(36) = (8)/(36) = (2)/(9) The transition n_2=3 to n_1=1 for the H-atom yields (8)/(9), which matches the value calculated for Li^2+. The final answer is 3 Drop the next question 📸