In which phase transition do molecules directly move from state to state involving a vibration of particles in a fixed position to a state involving random movement of high speed particles
evaporation
sublimation
freezing
depostion

Answer : The correct option is, Sublimation.

Explanation :

Solid state : It is a state in which the particles are closely packed and does not have any space between them. The intermolecular force of attraction between the particles are more.

Liquid state : It is a state in which the particles are present in random and irregular pattern. The particles are closely arranged. The intermolecular force of attraction between the particles are lower than solid.

Gaseous state : It is a state in which the particles are loosely arranged and have a lot of space between them. The intermolecular force of attraction between the particles are very low.

There are 6 phase changing process:

Melting or fusion : It is a type of process in which the phase changes from solid state to liquid state at constant temperature.  That means, phase changes from vibration of particles in a fixed position to a state involving random movement of particles.

Freezing : It is a type of process in which the phase changes from liquid state to solid state at constant temperature.  That means, phase changes from vibration of particles in a random position to a state involving fixed movement of particles.

Evaporation : It is a type of process in which the phase changes from liquid state to gaseous state at constant temperature.  That means, phase changes from vibration of particles in a less random position to a state involving more random movement of particles.

Condensation : It is a type of process in which the phase changes from gaseous state to liquid state at constant temperature.  That means, phase changes from vibration of particles in a more random position to a state involving less random movement of particles.

Sublimation : It is a type of process in which the phase changes from solid state to gaseous state without passing through the liquid state at constant temperature.  That means, phase changes from vibration of particles in a fixed position to a state involving random movement of high speed particles.

Deposition : It is a type of process in which the phase changes from gaseous state to solid state without passing through the liquid state at constant temperature.  That means, phase changes from vibration of particles in a random position to a state involving fixed movement of low speed particles.

Hence, the correct option is, Sublimation.

the element is Ca with atomic number 20