Question

The transition temperature of the mercury with an atomic mass 200 60 amu is 4.16k determine the transistion temperature of one of isotopes mass 204 amu

Answer 1

Answer:

The critical temperature of mercury for its isotope of mass 204 amu = 4.118 K

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Explanation:

Answer 2

Answer:

The transition temperature of mercury with isotopic mass 204 amu is 4.181K.

Transition Temperature:

• The temperature at which a sudden change in the physical properties of the material occurs is called transition temperature.
• It is also called the critical temperature.
• The sudden change can be a change in phase or crystalline state.
• The transition temperature is different for different materials.
• The transition temperature is proportional to the atomic mass.
• $T_{C}$∝$M^{-\beta }$, where $T_{C}$ is the transition temperature, M is the mass, and $\beta =0.5$

Explanation:

Given: $T_{1}=4.16K$, $M_{1}=200.60amu$, $M_{2}=204amu$

To find: Transition temperature $T_{2}$

Formula: $T_{C}$ ∝ $M^{-\beta }$

Step 1:

$T_{C}$ ∝ $M^{-\beta }$

$T_{1}=M_{1} ^{-\beta }$

$4.16=200.60 ^{-\beta }$

$ln(4.16)=-\beta ln(200.60)$

$1.426=-\beta (5.301)$

$\beta =-0.269$

Step 2:

Substituting the value of β and the given values,

$T_{2}=M_{2} ^{-\beta }$

$T_{2}=204 ^{-(-0.269) }$

$T_{2}=204 ^{0.269 }$

$T_{2}=4.181K$

Therefore, the transition temperature is 4.181K.

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