If an electron is localized in space ,its momentum becoms uncertain.If it is localized in time ,its energy becomes uncertain.explain this statement.
Look up the Heisenberg Uncertainty Principle
To understand this statement, we need to delve into the principles of quantum mechanics, specifically the Heisenberg uncertainty principle.
The Heisenberg uncertainty principle states that there is a fundamental limit to the precision with which we can simultaneously determine certain pairs of physical properties of a particle. One such pair is position and momentum, while another is time and energy.
When we say that an electron is localized in space, it means that we can determine its position with a high degree of certainty. However, according to the uncertainty principle, this precise knowledge of position comes at the expense of the momentum becoming uncertain.
To put it simply, the more precisely we try to determine the electron's position, the less we know about its momentum. This is not a limitation of our measurement tools but is inherent to the nature of quantum mechanics.
Similarly, if we try to localize an electron in time, that is, determine its energy with high precision, we encounter a similar trade-off. The more we try to limit the uncertainty in energy, the less certain we can be about the precise time at which the energy measurement occurs.
Therefore, when we attempt to precisely localize an electron either in space or time, the uncertainty principle tells us that we will face limitations in the determination of its complementary property – momentum or energy, respectively.
So, in summary, if we try to localize an electron in space, its momentum becomes uncertain due to the Heisenberg uncertainty principle. Likewise, if we try to localize it in time, its energy becomes uncertain. This trade-off is a fundamental feature of quantum mechanics and is a consequence of the wave-particle duality exhibited by quantum particles like electrons.