Question

An electon in a box absorbs light. The longest wavelength in the absorbtion spectrum is 700 nm . How long is the box

Answer 1

The question is about calculating the length of a box in which an electron is confined, based on the longest wavelength of light that it can absorb, 700 nm. It requires knowledge of quantum physics and application of the 'particle in a box' quantum mechanics model to estimate the box size, involving calculations that relate energy levels, wavelength, and frequency.

Step-by-step explanation:

The question involves determining the length of a box based on the longest wavelength of light that an electron confined within the box can absorb. This is a problem that involves understanding concepts from quantum mechanics, specifically concerning the quantization of energy levels in a confined system, which is known as the 'particle in a box' model in quantum physics.

The wavelength mentioned in the question, 700 nm, is associated with the absorption spectrum of the electron within this theoretical box, and the question implies that this wavelength corresponds to the transition from the ground state to the first excited state. Given this, and using the relevant principles from quantum mechanics, such as the wavenumber associated with a quantum transition, one can estimate the size of the box. Due to the complexity of the calculations and quantum mechanics concepts involved, the exact methodology to determine the box's length would typically require use of the formula for the energy levels of a 'particle in a box' and the relationship between energy, wavelength, and frequency of absorbed or emitted light.

Answer 2

8.01 (10^-10) m

Step-by-step explanation:

use the Particle in a box equation

E = (n^2) (h^2) / (8 m (L^2))

and energy of a particle as its wavelength equation

h c / lamda = E

combine the equations to get

h c / lamda = (n^2) (h^2) / (8 m (L^2))

get L alone

L^2 = (2^2 - 1^2) h lamda / 8 m c

the longest wavelength is produced by a jump from the first excited state to the ground so

n = 2 to n = 1

so

L^2 = (n1^2 - n2^2) h lamda / (8 m c)

h = 6.6(10^-34) J*s

c = 3(10^8) m/s

m = 9(10^-31) kg

lamda = 700(10^-9) m

n1 =2

n2=1