An electron in the 5th energy level of the H atom drops to the 3th energy level. In other words an electron in an excited state drops to a less excited state. What is the energy (in J) of the emitted photon

1.55 * 10-¹⁹ J

Explanation:

Using Rydberg's equation to calculate the wavelength of the transition of the photon from N = 5 to N = 3,

1/y = R [1/n²(final) - 1/n²(initial)]

y = wavelength (y is not the traditional sign of the Greek alphabet lambda, but however due to some restrictions currently, I'll be using letter "y" to represent lambda in my calculation)

R = Rydberg's constant = 1.0974 * 10-⁷ m-¹

1/y = 1.0974 * 10⁷ * [1/3³ - 1/5²]

1/y = 7.80 * 10⁵ m-¹

y = 1.28 * 10-⁶ m

Using energy-wavelength relationship,

E= hc/y

h = plank's constant

c = speed of light

y = wavelength

E = energy

E = (6.626 * 10-³⁴ * 3.0 * 10⁸) / 1.28 * 10-⁶

E = 1.55 * 10-¹⁹ J

Energy dissipated during the transition was 1.55 * 10-¹⁹ J

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

the answer would be a