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daser333 [38]
3 years ago
14

Consider an electron with charge −e and mass m orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e.

In the classical model, the electron orbits around the nucleus, being held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much like planets orbit around the sun, being held in orbit by their gravitational interaction. When the electron is in a circular orbit, it must meet the condition for circular motion: The magnitude of the net force toward the center, Fc, is equal to mv 2/r. Given these two pieces of information, deduce the velocity v of the electron as it orbits around the nucleus.
Physics
1 answer:
alexandr1967 [171]3 years ago
7 0

Answer:

v=\sqrt{k\frac{e^2}{m_e r}}, 2.18\cdot 10^6 m/s

Explanation:

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

k\frac{(e)(e)}{r^2}=m_e \frac{v^2}{r}

where

k is the Coulomb constant

e is the magnitude of the charge of the electron

e is the magnitude of the charge of the proton in the nucleus

r is the distance between the electron and the nucleus

v is the speed of the electron

m_e is the mass of the electron

Solving for v, we find

v=\sqrt{k\frac{e^2}{m_e r}}

Inside an atom of hydrogen, the distance between the electron and the nucleus is approximately

r=5.3\cdot 10^{-11}m

while the electron mass is

m_e = 9.11\cdot 10^{-31}kg

and the charge is

e=1.6\cdot 10^{-19} C

Substituting into the formula, we find

v=\sqrt{(9\cdot 10^9 m/s) \frac{(1.6\cdot 10^{-19} C)^2}{(9.11\cdot 10^{-31} kg)(5.3\cdot 10^{-11} m)}}=2.18\cdot 10^6 m/s

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If 0.035pC of charge is transferred via the movement of Al3+ ions, how's many of these must be transferred in total? Please add
mr Goodwill [35]

Each Al^+^3 ion contains three extra protons. Hence, the extra charge on each  Al^+^3 = 3 \times 1.6 \times 10^-^1^9 C

Total charge = 0.035 pC

Total charge (Q) = 0.035 \times 10^-^1^2 C

Let the number of Al^+^3 ions be n.

According to question:

n \times 3 \times 1.6 \times 10^-^1^9 =0.035 \times 10^-^1^2

n = \frac{0.035 \times 10^-^1^2}{3 \times 1.6 \times 10^-^1^9}

n = 7.29167 \times 10^4

n = 72917

Hence, the total number of ions needed to be transferred is 72917

3 0
3 years ago
An apple hanging from a limb has potential energy because of its height . If it falls ,what becomes of this energy just before i
sineoko [7]

Answer: Just before its hits the ground it becomes kinetic energy and when it hits the ground it becomes in another form of energy (acoustic energy or thermal energy, for example)

Explanation:

Energy is the ability of matter to produce work in the form of movement, light, heat, among others.

In this sense, according to the Conservation of Energy principle: <em>"energy is not created or destroyed, it is transformed."</em>

So, in the case of the apple, its total energy is conserved.

When the apple is hanging from a limb, it has zero kinetic energy K_{o}=0 (because it is at rest) and has gravitational potential energy U_{o}, which depends on the mass m, the acceleration due gravity g and the height h:

U_{o}=mgh

When the apple falls, just before its hits the ground, this gravitational potential energy transforms in kinetic energy K_{1} (since the apple is moving), which depends on the mass and velocity V of the apple:

K_{1}=\frac{1}{2}mV^{2}

When the apple hits the ground, the gravitational potential energy is zero (h=0) and the kinetic energy transforms into some other form of energy (acoustic energy or thermal energy, for example).

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A 70-kg ice skater is standing still on the ice, when a friend tosses him a 10-kg ball that is traveling at +8 m/s. If he catche
Misha Larkins [42]

Answer:+1.25 m/s

Explanation:

Given

mass of ice skater M=70 kg

mass of ball m=10 kg

the initial velocity of the ball  u_1=+8\ m/s

Conserving linear momentum

M\times0+m\timesu_1=(M+m)v\quad \quad [v=\text{combined velocity of skater and ball}]

v=\dfrac{10\times10}{80}=+1.25\ m/s

Therefore the velocity of the person holding the ball is 1.25 m/s

This collision represents the perfectly inelastic collision where particles stick together after the collision.

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Learn more about the universe here:

brainly.com/question/8705671

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