When an electron transitions to a higher energy level within an atom, its speed around the nucleus does not change in a simple sense. The movement of an electron in an atom is described by its wave function, which represents its probability distribution in space. It is not accurate to envision the electron as a tiny particle orbiting the nucleus in a classical sense.
However, it is important to note that as the electron moves to a higher energy level, its average distance from the nucleus increases. This means that the electron is more likely to be found farther away from the nucleus compared to its original energy level. The distribution of the electron's probable positions becomes more spread out.
In terms of the speed of the electron, it is related to its energy. When an electron absorbs energy and transitions to a higher energy level, its energy increases. According to the principles of quantum mechanics, the energy of an electron in an atom is quantized, meaning it can only have specific discrete energy levels. The exact relationship between energy and speed in quantum mechanics is more complex than the classical concept of speed in everyday objects.
Therefore, it is more accurate to say that as an electron moves to a higher energy level, its average distance from the nucleus increases, rather than its speed around the nucleus changing in a simple manner.