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Dmitry_Shevchenko [17]
3 years ago
13

Using Planck’s constant as h = 6.63 E-34 J*s, what is the wavelength of a proton with a speed of 5.00 E6 m/s? The mass of a prot

on is 1.66 E-27 kg.
Remember to identify your data, show your work, and report the answer using the correct number of significant digits and units.
Physics
1 answer:
Marrrta [24]3 years ago
6 0
De Broglie's identity gives the relationship between the momentum and the wavelength of a particle:
p=mv= \frac{h}{\lambda}
where
p is the particle momentum
m is its mass
v its velocity
h is the Planck constant
\lambda is the wavelength

By re-arranging the equation, we get
\lambda=  \frac{h}{mv}
and by using the data about the proton, given in the text, we can find the proton's wavelength:
\lambda= \frac{h}{mv} = \frac{6.63 \cdot 10^{-34} Js}{(1.66 \cdot 10^{-27} kg)(5.00 \cdot 10^6 m/s)} =7.99 \cdot 10^{-14} m
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Answer:

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Explanation:

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Re-arranging the equation, we have

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Dividing through by m, we have

d²x/dt² + (b/m)dx/dt + (k/m)x = 0

This is a second-order differential equation. The characteristic equation is thus,

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Using the quadratic formula, we find D.

D = \frac{-(b/m) +/- \sqrt{(b/m)^{2} - 4k/m} }{2}

For an overdamped system,

(b/m)^{2} - 4k/m} >   0

(b/m)^{2} >   4k/m}\\(b/m) >   \sqrt{4k/m}} \\(b/m) >   2\sqrt{k/m}} \\b >   2\sqrt{km}}

Now, k = F/x. Since the weight of the object causes the spring to stretch a distance of 0.5 m, k = mg/x where m = mass of object = 0.75 kg, g = 9.8 m/s² and x = x₀ =0.5 m.

Substituting k = mg/x into the inequality for b, we have

b > 2√{(mg/x₀)m}

b > 2√{(m²g/x₀)}

b > 2m√{g/x₀)}

b > 2 × 0.75 kg√{9.8 m/s²/0.5 m)}

b > 1.5 kg√{19.6/s²)}

b > 1.5 kg × 4.427/s

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