Physics, 19.03.2020 21:22 ayoismeisalex

The mass of an electron is 9.11×10−31 kg9.11×10−31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31×10−10 m3.31×10−10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00×108 m/s3.00×108 m/s. Express your answer numerically as a percent.

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Answer from: tayjohn9774

The speed of electron is 0.73 % of the speed of light.

Explanation:

Given that,

Mass of the electron, $m=9.1\times 10^{-31}\ kg$

De- Broglie wavelength of the electron, $\lambda=3.31\times 10^{-10}\ m$

Speed of light, $c=3\times 10^8\ m/s$

The De Broglie wavelength of the electron is given by the formula as follows :

$\lambda=\dfrac{h}{mv}\\\\v=\dfrac{h}{m\lambda}\\\\v=\dfrac{6.63\times 10^{-34}}{9.11\times 10^{-31}\times 3.31\times 10^{-10}}\\\\v=2.19\times 10^6\ m/s$

The electron moving relative to the speed of light is calculated as :

$=\dfrac{v}{c}\times 100\\\\=\dfrac{2.19\times 10^6}{3\times 10^8}\times 100\\\\=0.73$

So, the speed of electron is 0.73 % of the speed of light. Hence, this is the required solution.

Answer from: Quest

Ineed the problem dude

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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The mass of an electron is 9.11×10−31 kg9.11×10−31 kg. If the de Broglie wavelength for an electron...

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