An intuitive way is to think of matter waves. If the electron were a point particle, it would have to start from a definite position, say somwewhere on its orbit, and all of it would feel the electric attraction to the nucleus and it would start falling just like a stone. It could not find a stable orbit like the moon does since it is charged and whenever it accelerates it gives off electromagnetic radiation, like in a radio antenna transmitting radio waves. But then it loses energy, and cannot maintain its orbit.

The only solution to this is if the electron can somehow stand still. (Or achieve escape velocity, but of course you are asking about the electrons in the atom, so by hypothesis, they have not got enough energy to achieve escape velocity.) But if it stands still and is a point particle, of course it will head straight to the nucleus because of the attraction.

Answer: matter is not made of point particles, but of matter waves. These matter waves obey a wave equation. The point of any wave equation, such as $${\partial^2f\over \partial t^2} = - k \;{\partial^2f\over \partial x^2}$$ (this, if $k$ is negative, is the wave equation for a stretched and vibrating string) is that the right hand side is the curvature of the wave at the spot $x$, and the equation says the greater the curvature, the greater is the rate of change of the wave at that spot (or, in this case, the acceleration, but Schroedinger used a slightly different wave equation than de Broglie or Fock), and hence the kinetic energy, too.

There are certain shapes which just balance everything out: for example, the lowest orbital is a humpy shape with centre at the centre of the nucleus, and thinning out in all directions like a bell curve or a hill. Although all the parts of the smeared-out electron might feel attracted to the nucleus, there is a sort of effect which is purely quantum mechanical, a consequence of this wave equation, which resists that: if all parts approached the nucleus, the hump becomes more acute, a sharper, higher peak, but this increases the left hand side of the equation (greater curvature). This would increase the magnitude of the right hand side, and that greater motion tends to disperse the peak again. So the electron wave, in this particular stationary state, stays where it is because this quantum mechanical resistance exactly balances out the Coulomb force.

This is why Quantum Mechanics is necessary in order to explain the stability of matter, something which cannot be understood if everything were made of mass as particles with definite locations.

An intuitive way is to think of matter waves. If the electron were a point particle, it would have to start from a definite position, say somewhere on its orbit, and all of it would feel the electric attraction to the nucleus and it would start falling just like a stone. It could not find a stable orbit like the moon does since it is charged and whenever it accelerates it gives off electromagnetic radiation, like in a radio antenna transmitting radio waves. But then it loses energy, and cannot maintain its orbit.

The only solution to this is if the electron can somehow stand still. (Or achieve escape velocity, but of course you are asking about the electrons in the atom, so by hypothesis, they have not got enough energy to achieve escape velocity.) But if it stands still and is a point particle, of course it will head straight to the nucleus because of the attraction.

Answer: matter is not made of point particles, but of matter waves. These matter waves obey a wave equation. The point of any wave equation, such as $${\partial^2f\over \partial t^2} = - k \;{\partial^2f\over \partial x^2}$$ (this, if $k$ is negative, is the wave equation for a stretched and vibrating string) is that the right hand side is the curvature of the wave at the spot $x$, and the equation says the greater the curvature, the greater is the rate of change of the wave at that spot (or, in this case, the acceleration, but Schrödinger used a slightly different wave equation than de Broglie or Fock), and hence the kinetic energy, too.

There are certain shapes which just balance everything out: for example, the lowest orbital is a humpy shape with centre at the centre of the nucleus, and thinning out in all directions like a bell curve or a hill. Although all the parts of the smeared-out electron might feel attracted to the nucleus, there is a sort of effect which is purely quantum mechanical, a consequence of this wave equation, which resists that: if all parts approached the nucleus, the hump becomes more acute, a sharper, higher peak, but this increases the left hand side of the equation (greater curvature). This would increase the magnitude of the right hand side, and that greater motion tends to disperse the peak again. So the electron wave, in this particular stationary state, stays where it is because this quantum mechanical resistance exactly balances out the Coulomb force.

This is why quantum mechanics is necessary in order to explain the stability of matter, something which cannot be understood if everything were made of mass as particles with definite locations.

An intuitive way is to think of matter waves. If the electron were a point particle, it would have to start from a definite position, say somwewhere on its orbit, and all of it would feel the electric attraction to the nucleus and it would start falling just like a stone. It could not find a stable orbit like the moon does since it is charged and whenever it accelerates it gives off electromagnetic radiation, like in a radio antenna transmitting radio waves. But then it loses energy, and cannot maintain its orbit.

The only solution to this is if the electron can somehow stand still. (Or achieve escape velocity, but of course you are asking about the electrons in the atom, so by hypothesis, they have not got enough energy to achieve escape velocity.) But if it stands still and is a point particle, of course it will head straight to the nucleus because of the attraction.

Answer: matter is not made of point particles, but of matter waves. These matter waves obey a wave equation. The point of any wave equation, such as $${\partial^2f\over \partial t^2} = - k {\partial^2f\over \partial x^2}$$ (this, if $k$ is negative, is the wave equation for a stretched and vibrating string) is that the right hand side is the curvature of the wave at the spot $x$, and the equation says the greater the curvature, the greater is the rate of change of the wave at that spot (or, in this case, the acceleration, but Schrodinger used a slightly different wave equation than de Broglie or Fock), and hence the kinetic energy, too.

There are certain shapes which just balance everything out: for example, the lowest orbital is a humpy shape with centre at the centre of the nucleus, and thinning out in all directions like a bell curve or a hill. Although all the parts of the smeared-out electron might feel attracted to the nucleus, there is a sort of effect which is purely quantum mechanical, a consequence of this wave equation, which resists that: if all parts approached the nucleus, the hump becomes more acute, a sharper, higher peak, but this increases the left hand side of the equation (greater curvature). This would increase the magnitude of the right hand side, and that greater motion tends to disperse the peak again. So the electron wave, in this particular stationary state, stays where it is because this quantum mechanical resistance exactly balances out the Coulomb force.

This is why Quantum Mechanics is necessary in order to explain the stability of matter, something which cannot be understood if everything were made of mass as particles with definite locations.

An intuitive way is to think of matter waves. If the electron were a point particle, it would have to start from a definite position, say somwewhere on its orbit, and all of it would feel the electric attraction to the nucleus and it would start falling just like a stone. It could not find a stable orbit like the moon does since it is charged and whenever it accelerates it gives off electromagnetic radiation, like in a radio antenna transmitting radio waves. But then it loses energy, and cannot maintain its orbit.

The only solution to this is if the electron can somehow stand still. (Or achieve escape velocity, but of course you are asking about the electrons in the atom, so by hypothesis, they have not got enough energy to achieve escape velocity.) But if it stands still and is a point particle, of course it will head straight to the nucleus because of the attraction.

Answer: matter is not made of point particles, but of matter waves. These matter waves obey a wave equation. The point of any wave equation, such as $${\partial^2f\over \partial t^2} = - k \;{\partial^2f\over \partial x^2}$$ (this, if $k$ is negative, is the wave equation for a stretched and vibrating string) is that the right hand side is the curvature of the wave at the spot $x$, and the equation says the greater the curvature, the greater is the rate of change of the wave at that spot (or, in this case, the acceleration, but Schroedinger used a slightly different wave equation than de Broglie or Fock), and hence the kinetic energy, too.

There are certain shapes which just balance everything out: for example, the lowest orbital is a humpy shape with centre at the centre of the nucleus, and thinning out in all directions like a bell curve or a hill. Although all the parts of the smeared-out electron might feel attracted to the nucleus, there is a sort of effect which is purely quantum mechanical, a consequence of this wave equation, which resists that: if all parts approached the nucleus, the hump becomes more acute, a sharper, higher peak, but this increases the left hand side of the equation (greater curvature). This would increase the magnitude of the right hand side, and that greater motion tends to disperse the peak again. So the electron wave, in this particular stationary state, stays where it is because this quantum mechanical resistance exactly balances out the Coulomb force.

This is why Quantum Mechanics is necessary in order to explain the stability of matter, something which cannot be understood if everything were made of mass as particles with definite locations.