An electron in the n = 6 level emits a photon with a wavelength of 410.2 nm. to what energy level does the electron move? <

Question

An electron in the n = 6 level emits a photon with a wavelength of 410.2 nm. to what energy level does the electron move?

a. n = 1

b. n = 2

c. n = 3

d. n = 4

e. n = 5

in progress 0
Thiên Thanh 5 years 2021-07-26T05:25:34+00:00 2 Answers 574 views 0

Answers ( )

  1. thachthao
    0
    2021-07-26T05:27:16+00:00
    Reply

    Answer:

    b. n = 2

    Explanation:

    To find the energy level you use the following formula from the Bohr’s model:

    \Delta E=-13.6(\frac{1}{n_2^2}-\frac{1}{n_1^2})   (1)

    n2: initial state

    n1: final state

    To find the final state n2, is necessary to calculate the change in energy. This is made by using the following formula:

    \Delta E=h\nu=h\frac{c}{\lambda}

    h: Planck’s constant = 6.62*10^⁻34Js

    By replacing you obtain:

    \Delta E=(6.62*10^{-34}Js)\frac{3*10^8m/s}{410.2*10^{-9}m}=4.841*10^{-19}J

    4.841*10^{-19}(6.242*10^{18}eV)=3.022eV (to use the formula (1) the unit of energy must be eV).

    Finally, by doing n1 the subject of the formula (1) you obtain:

    \Delta E+\frac{13.6}{n_2^2}=\frac{13.6}{n_1^2}\\\\n_1=\sqrt{\frac{13.6}{\Delta E+\frac{13.6}{n_2^2}}}=\sqrt{\frac{13.6}{3.022+\frac{13.6}{6^2}}}=2

    hence, the electron moves to the n=2 level

  2. trungdung22
    0
    2021-07-26T05:27:25+00:00
    Reply

    Answer:

    It drops to energy level 2. Hence, answer is B

    Explanation:

    Using Rydberg’s formula to find the lower level.

    The formula is:

    1/w = R(1/L² – 1/U²), where w is the wavelength in meters, L is

    the lower energy level ( which is what we want to find),

    U is the upper level = 6

    R is Rydberg’s constant =10,967,758 waves per meter for hydrogen.

    Substituting values into the formula, we obtain: 1/(4.102 * 10**-7) = 10967759(1/L² – 1/36)

    Change to decimal fractions for easier calculation and we get:

    2437835 = 10967758(1/L² – 0.02777777) Divide both sides by 10967758 and

    we obtain: 0.222273 = 1/L² – 0.02777777 Now add 0.0277777 to both sides

    and obtain 0.250005 = 1/L²

    Since 0.250005 is very close to ¼

    Hence, we have

    1/L² = ¼ so L² = 4 and L = 2.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )