I need solve this question

Problem 2 (30 points) A microscopic spring-mass system has a mass m = 5 x 10 2 kg and the energy gap between the 2nd and 3rd excited states is 7 eV. a) (2 points) Calculate in joules, the energy gap between the Ist and 2nd excited states: E= b) (2 points) What is the energy gap between the 4th and 7th excited states: E= ev c) (1 point) To find the energy of the ground state, which equation can be used ? (check the formula_sheet and select the number of the equation) d) (1 point) Which of the following substitutions can be used to calculate the energy of the ground state? O- 7 O2 X 7 (6.582x10-16) 2 2 O(6. 582 x 10-16 ) (7) 0% (6.582 x 10-16) (7) e) (3 points) The energy of the ground state is: E= ev f) (1 point) To find the stiffness of the spring, which equation can be used ? (check the formula_sheet and select the number of the equation) g) (1 point) Which of the following substitutions can be used to calculate the stiffness of the spring? 6.582x10-16 5X10-26 O(5 x 10-26) 7 6.582x10-16 O(5 x 10-26 ) 7 6.582x10-16 -6.582X10-16 5x10-26 O(5 x 10-26 ) (7)2 O(5 x 10-26 ) (6. 582 x 10-16) 2 O2- (6.582x10-16) 2 h) (3 points) The stiffness of the spring is: K = (N/m) i) (2 point) What is the smallest amount of vibrational energy that can be added to this system? E = ev