Question

In a hydrogen atom, the electron and the proton are seperated by about 0.5 angstroms, 5.0×10−11 m. what is the acceleration of an electron in this atom?

Answer 1

The charge of proton and electron is equal in magnitude that is $1.6\times 10^{-19} C$. The distance between electron and proton is $0.5 \AA$ or $5\times 10^{-11} m$.

Force exerted on electron by proton is calculated as follows:

$F= \left | \frac{kq_{e}q_{p}}{r^{2}} \right |$

Here, k is Coulomb's constant, $q_{p}$ is charge on proton,  $q_{e}$ charge on electron and r is distance between them.

Putting the values,

$F= \left | \frac{(8.99\times 10^{9}N m^{2}/C^{2})(1.6\times 10^{-19} C)(1.6\times 10^{-19} C)}{(5\times 10^{-11} m)^{2}} \right |=9.2\times 10^{-8} N$

Now, according to second law of Newton,

$F=m_{e}a$

Here, $m_{e}$ is mass of electron and a is acceleration.

Also, $1 N=1 kgm/s^{2}$

Rearranging,

$a=\frac{F}{m_{e}}=\frac{9.2\times 10^{-8} Kg m/s^{2}}{9.11\times 10^{-31} kg}=1.01\times 10^{23} m/s^{2}$

Thus, the acceleration of an electron in this atom is $1.01\times 10^{23} m/s^{2}$.

Answer 2

The acceleration of an electron in this atom = a = 1.009.10²⁰ m/s²

Further explanation

Rutherford scientists experimented with firing alpha rays on a thin gold plate

From here comes the Rutherford atomic model which states that the initiate consists of positively charged particles and negatively charged electrons around the nucleus

Inside the atom consists of a nucleus containing 3 basic particles namely protons and neutrons, while electrons move around the nucleus.

The charge of 1 proton is equal to a charge of 1 electron, but the sign is different.

The proton is positively charged (+1), the electron is negatively charged (-1). and neutrons not charged (neutral)

For a charge of 1 electron = e = 1.66.10⁻¹⁹ coulomb

Whereas the neutron charge = 0

This atomic unit uses the standard atomic mass, that is, the C-12 isotope

1 C-12 atom = 12 atomic mass units

1 atomic mass unit = 1/12 x mass 1 atom C-12

The mass of 1 proton is equal to the mass of 1 neutron, equal to 1 atomic mass unit and electrons have a smaller mass than both.

electron mass = 9.11.10-28 g

proton mass = 1.6726.10-24 g

neutron mass = 1,675.10-24 g

Coulomb stated the law that between two points / charged particles with a certain distance there is a force that arises between the two points

This style can repel or attract each other

Can be formulated

$\large{\boxed{\bold{F=\frac{k.Q1.Q2}{r^2}}}}$

k =  8.99 x 10⁹ Nm² / C²

While the electron charge = proton charge = 1.60 x 10⁻¹⁹ C

While the distance from the proton and electron is: 5.0 × 10¹¹ m

So the style that arises is:

F =  8.99 x 10⁹. (1.60 x 10⁻¹⁹)² / (5.0 × 10¹¹)²

F = 9.2.10⁻⁸

Then the acceleration of an electron, from Newtton's Law

a = F/m

a =  9.2.10⁻⁸/ 9.11.10⁻²⁸ g

a = 1.009.10²⁰ m/s²

Learn more

resultant velocity

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Electromagnetic radiation

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Bohr's model of the atom

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Keywords : atom, electron, proton, acceleration