1) An electron, m = 9.109 × 10^-31 kg, is moving in a two...

1) An electron, $m = 9.109 \times 10^{-31}$ kg, is moving in a two dimensional box. The frequency of the $n$ \$= 1$ to $n = 2$ transition is $6 \times 10^{12}$/sec. A) What is the length of the box? B) What wavelength of light is emitted if the electron transits from $n = 4$ to $n = 2$?

Transcript

00:03 Question 93 is an application question from information presented in this chapter.

00:10 However, in this question, it also provides some additional information, and most specifically, an equation that is used to describe the energy of an electron confined to a one -dimensional box.

00:25 The equation that is provided is the energy is going to be equal to a quantum number, n, which could be an integer, 1, 2, 3, and so forth.

00:37 Squared, multiplied by planck's constant, squared, divided by 8, and in the denominator also the mass of the electron, and then the length of the box, the one -dimensional box.

00:53 The length was given to us as 155 picometers.

00:58 Pico means 1 times 10 to the negative 12.

01:01 H is planck's constant at 6 .62 .2.

01:04 10 to negative 34.

01:06 The mass of an electron we can look up it's 9 .109 times 10 to negative 31 and then as i mentioned the length of the box is 155 pico meaning 10 to the negative 12 meters.

01:19 So all we have to do is plug in n at 1, 2, and 3 in order to calculate the energy of an electron in these quantum states 1, 2, and 3.

01:32 For the energy of the electron in this box in the first quantum state it has 2 .51 times 10 to the negative 18 joules.

01:47 You will notice with this equation all we're going to replace is n up here.

01:52 So we're going to go from 1 squared to the second energy level 2 squared...

Question

1) An electron, $m = 9.109 \times 10^{-31}$ kg, is moving in a two dimensional box. The frequency of the $n$ \$= 1$ to $n = 2$ transition is $6 \times 10^{12}$/sec. A) What is the length of the box? B) What wavelength of light is emitted if the electron transits from $n = 4$ to $n = 2$?

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