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Question: The susceptibility of magnesium at 300 K is 1.2 \(\times 10^{-5}\) at what temperature the susceptib...

The susceptibility of magnesium at 300 K is 1.2 ×10−5\times 10^{-5} at what temperature the susceptibility will increase to 1.8 ×10−5\times 10^{-5}.

Explanation

Solution

The susceptibility of a magnetic material is defined as the ratio of the magnetization vector (M), and the applied magnetic field. The magnetic susceptibility gives the measure of how much the material gets magnetized upon application of applied magnetic field.
Formula used:
The magnetic susceptibility of a material at temperature T is given as:
Xm=CTX_m = \dfrac{C}{T} .

Complete answer:
Curie law states that the magnetic susceptibility is inversely proportional to the temperature of the material. This can be expressed mathematically as:
Xm=CTX_m = \dfrac{C}{T} .
Now, we first substitute the known values here to get C,
C=1.2×10−5×300=3.6×10−3KAT−1m−1C = 1.2 \times 10^{-5} \times 300 = 3.6 \times 10^{-3} K A T^{-1} m^{-1} .
The temperature can be calculated as:
T=CXmT = \dfrac{C}{ X_m }
Keeping the values here we get:
T=3.6×10−31.8×10−5=200T = \dfrac{3.6 \times 10^{-3}}{ 1.8 \times 10^{-5} } = 200 K.
The temperature decreases and becomes 200 K when the susceptibility increases to 1.8 ×10−5\times 10^{-5}.

Additional Information:
The magnetic properties of a material get affected as a substance is heated. A ferromagnetic substance can become a paramagnetic substance when heated at high enough temperatures. A paramagnet is a weakly attractive material and a ferromagnet is a material that retains its magnetic properties even when the magnetic field is removed. A paramagnet only gets attracted towards regions of strong magnetic field when the magnetic field is applied. As soon as the field is removed, the magnetic properties are gone.

Note:
One cannot substitute the temperature in degree Celsius here. The magnetic susceptibility is inversely proportional to the absolute temperature of the material in Kelvins. Generally at a temperature where the magnetic property of material changes from ferromagnetic to paramagnetic. Knowing this, one can know the trend as to whether the susceptible increases or decreases with temperature.