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3 years ago

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A laser beam of unknown wavelength passes through adiffraction grating having 5510 lines/cm after striking itperpendicularly. Ta

king measurements, you find that the first pairof bright spots away from the central maximum occurs at±15.4° with respect to the original beam direction. (a) What is the wavelength of thelight? (b) at what angle will the next pair ofbright spots occur?

1 answer:

Ivahew [28]3 years ago

7 0

Answer:

Explanation:

distance between two slit d = $\frac{1 \times 10^{-2}}{5510}$

d = 18.15 x 10⁻⁷ m

Let wave length of light λ

formula for position of first pair of bright spot

Tanθ = λ / d , λ is wave length of light and d is distance between two slit .

Tan 15.4 = $\frac{\lambda}{18.15\times10^{-7}}$

λ = Tan 15.4 x 18.15 x 10⁻⁷

=5 x 10⁻⁷ m

If θ be the position of next bright spot

Tanθ = 2 λ / d

= $\frac{2 \times\ 5\times\ 10^ {-7}}{18.15\times10^{-7}}$

= $\frac{2\times5}{18.5}$

θ = 28.4 degree .

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Explanation:

The magnitude of the electromagnetic force between the electron and the proton in the nucleus is equal to the centripetal force:

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Answer:

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b) $v_{max}=6.283\frac{m}{s}$

c) $E=0.1974J$

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Explanation:

1) Important concepts

Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".

2) Part a

The equation that describes the simple armonic motion is given by $X=Acos(\omega t +\phi)$ (1)

And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.

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$\omega =\sqrt{\frac{8000\frac{m}{s^2}}{0.002m}}=2000\frac{rad}{s}$

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From equation (2) we see that the maximum velocity occurs when the sine function is euqal to -1 and on this case we have that:

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In order to find the total mechanical energy of the oscillator we can use this formula:

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$|\frac{d^2X}{dt^2}|=A\omega^2 cos(\omega t +\phi)=A\omega^2 \frac{1}{2}$

And the force would be given by:

$F=ma=\frac{1}{2}mA\omega^2$

And replacing we have:

$F=\frac{1}{2}(0.01Kg)(0.002m)(2000\frac{rad}{s})^2 =40N$

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