For atomic hydrogen, the Paschen series of lines occurs when nf = 3, whereas the Brackett series occurs when nf = 4 in the equation 1 λ = 2π2mk2e4 h3c (Z2) 1 n2f − 1 n2i . Using this equation, show that the ranges of wavelengths in these two series overlap.

a straight line sloped

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.