Question

You discover a new type of microscopic, atom-like object. The energy levels for this object are given by En = E1 n , where E1 = −28.0 eV. For this new object, determine the following.
(a) excitation energy (in eV) of the object in the third excited state
(b) amount of energy (in eV) required to cause an object in the third excited state to become unbound
(c) maximum number of different energy photons emitted as the object de-excites from the third excited state to the ground state (assuming all available transitions are possible)
(d) maximum and minimum wavelength photons (in nm) emitted when the object de-excites from the third excited state to the ground state

Answer 1

Answer:

a) Excitation energy for the third excited state = -112 eV

b) The amount of energy required to cause an object in the third excited state to become unbound = 112 eV

c) Max number of photons emitted as the object de - excites from the third excited state to the ground state = 6

d) Maximum wavelength photons = 532.286 nm

Minimum wavelength photons = 59.14 nm

Explanation:

From the question, the energy levels are given by $E_{n} = E_{1} n$

Where the energy level for the ground state is given by $E_{1} = -28.0 eV$

a) Excitation energy for the third excited state, n = 4

$E_{4} = 4 * E_{1}$

$E_{4} = -28 * 4$

$E_{4} = -112 eV$

b) The amount of energy required to cause an object in the third excited state to become unbound

$E_{4} = 112 eV$

c) Max number of photons emitted = $\frac{n(n-1)}{2}$

Max number of photons emitted  = $\frac{4(4-1)}{2}$

Max number of photons emitted  = 2 * 3 = 6

d) $\frac{1}{\lambda_{max} } = \frac{28}{hc} [\frac{1}{3} -\frac{1}{4}]$

$hc = 1242 eV-nm$

$\frac{1}{\lambda_{max} } = \frac{28}{1242} [\frac{1}{3} -\frac{1}{4}]$

$\lambda_{max} = 532.286 nm$

Maximum wavelength photons = 532.286 nm

$\frac{1}{\lambda_{min} } = \frac{28}{hc} [\frac{1}{1} -\frac{1}{4}]$

$\frac{1}{\lambda_{min} } = \frac{28}{1242} [\frac{1}{1} -\frac{1}{4}]$

$\lambda_{min} = 59.14 nm$

Minimum wavelength photons = 59.14 nm