what is the temprature at which molecular motion ceases??
0 K
is the answer they want.
However, according to the uncertainty principle, there must be some residual motion and position uncertainty even at absolute zero.
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc4.html
The temperature at which molecular motion ceases, also known as absolute zero, is approximately -273.15 degrees Celsius or 0 Kelvin. It is the lowest temperature possible in the known universe.
To understand how absolute zero is determined, we need to know about the kinetic theory of gases. According to this theory, temperature is a measure of the average kinetic energy of particles in a substance. As the temperature decreases, the average kinetic energy decreases, resulting in slower particle motion.
In the late 18th century, scientists began to study the relationship between temperature and gas pressure. By cooling gases and observing the reduction in pressure, they found that as the temperature approached absolute zero, the pressure of the gas would approach zero as well.
The concept of absolute zero was further developed in the 19th century by Lord Kelvin. He proposed an absolute temperature scale, now known as the Kelvin scale, where 0 Kelvin represents absolute zero. On the Kelvin scale, all temperatures are positive and directly proportional to the average kinetic energy of particles.
Reaching absolute zero in practice is challenging and has not been achieved yet. However, scientists have come close to achieving extremely low temperatures, a few billionths of a Kelvin above absolute zero, using advanced cooling techniques such as laser cooling and evaporative cooling.