Question

Be sure to answer all parts. Enter your answers in scientific notation.

The following values are the only allowable energy levels of a hypothetical one-electron atom:

E6 = −2.0×10−19 J

E5 = −7.0×10−19 J

E4 = −11.0×10−19 J

E3 = −15.0×10−19 J

E2 = −17.0×10−19 J

E1 = −20.0×10−19 J

(a) If the electron were in the n = 5 level, what would be the highest frequency (and minimum wavelength) of radiation that could be emitted?

Frequency-

Wavelength-

(b) If the electron were in the n = 1 level, what would be the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization?

Answer 1

a) f = 3.02x10¹⁵ s⁻¹, and λ = 99.4 nm.

b) 99.4 nm

Step-by-step explanation:

a) The energy of radiation is given by:

E = h*f

Where h is the Planck constant (6.626x10⁻³⁴ J.s), and f is the frequency. To have the highest frequency, the energy must be the highest too, because they're directly proportional. So we must use E = -E1 = 20x10⁻¹⁹ J

20x10⁻¹⁹ = 6.626x10⁻³⁴xf

f = 3.02x10¹⁵ s⁻¹

The wavelenght is the velocity of light (3.00x10⁸ m/s) divided by the frequency:

λ = 3.00x10⁸/3.02x10¹⁵

λ = 9.94x10⁻⁸ m = 99.4 nm

b) To have the shortest wavelength, it must be the highest energy and frequency, so it would be the same as the letter a) 99.4 nm.