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1 year ago

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

Physics

1 answer:

vova2212 [387]1 year ago

4 0

Answer:

8.01 (10^-10) m

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

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

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A carpenter builds an exterior house wall with a layer of wood 3.0 cm thick on the outside and a layer of Styrofoam insulation 2

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Answer:

A. T=15.54 °C

B. Q/A= 0.119 W/m2

Explanation:

To solve this problem we need to use the Fourier's law for thermal conduction:

$Q= kA\frac{dT}{dx}$

Here, the rate of flow per square meter must be the same through the complete wall. Therefore, we can use it to find the temperature at the plane where the wood meets the Styrofoam as follows:

$\frac{Q}{A} =\frac{T_1-T_0}{d_w}k_w=\frac{T_2-T_1}{d_s}k_s\\T_1(\frac{k_w}{d_w}+\frac{k_s}{d_s})=T_2\frac{k_s}{d_s}+T_0\frac{k_w}{d_w}\\T_1=\frac{T_2\frac{k_s}{d_s}+T_0\frac{k_w}{d_w}}{\frac{k_w}{d_w}+\frac{k_s}{d_s}}\\T_1= 15.54 \°C$

Then, to find the rate of heat flow per square meter, we have:

$\frac{Q}{A}=\frac{T_1-T_0}{d_w}k_w=0.119 \frac{W}{m^2}\\\frac{Q}{A}=\frac{T_2-T_1}{d_s}k_s= 0.119 \frac{W}{m^2}$

$T_0: Temperature \ in \ the \ house\\T_1: Temperature \ at \ the \ plane \ between \ wood \ and \ styrofoam\\T_2: Temperature \ outside\\k_w: k \ for \ wood\\d_w: wood \ thickness\\k_s: k \ for \ styrofoam\\d_s: styrofoam \ thickness$