Two adjacent allowed energies of an electron in a one-dimensional box are 5.4 ev and 9.6 ev. what is the length of the box?

E = energy in nth state = 5.4 eV

E' = energy in (n + 1)th state = 9.6 eV

L = length of the box

m = mass of electron = 9.1 x 10⁻³¹ kg

h = plank's constant = 6.63 x 10⁻³⁴

Energy in nth state is given as

E = n²h²/(8 m L²)                                              eq-1

Energy in (n+1) th state is given as

E' = (n + 1)²h²/(8 m L²)                                        eq-2

dividing eq-1 by eq-2

E/E' = n²/(n + 1)²

inserting the values

5.4 /9.6 = n²/(n + 1)²

n = 3

using eq-1

E = n²h²/(8 m L²)

inserting the values

5.4 x 1.6 x 10⁻¹⁹ = (3)² (6.63 x 10⁻³⁴)²/(8 (9.1 x 10⁻³¹) L²)

L = 7.9 x 10⁻¹⁰ m

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min

in order to follow the instructions and complete the statements, i need to use data from table c of your student guide. can you think of a way to let me see your student guide for a while ? i can't answer the question without the data in table c.