The Problem With Rutherford's Model of the Atom

Rutherford's model of the atom is still frequently taught today even though we as I'll explain later it's not quite correct however there was one fatal problem with Rutherford's model. According to Maxwell's equations which describe the electromagnetic force when you accelerate a charged particle and of course an electron is a charged particle it should emit light or electromagnetic radiation. But if electrons were constantly emitting electromagnetic radiation they would also be constantly losing energy meaning that they would constantly be slowing down as they traveled about the atom. This would be demonstrated by the electrons gradually spiraling into the neutron sorry to the nucleus as they lost energy and therefore traveled slower.