Which relation is wrong

To determine which relation is incorrect, let us analyze each of the given options one by one:

1. Checking the first relation: 1 Calorie = 4.18 Joules
A calorie is a unit of energy defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. The conversion factor between calories and Joules (the SI unit of energy) is approximately:
$1 \text{Calorie}\approx \mathrm{4.184} \text{Joules}$
Thus, the relation $1 \text{Calorie}=\mathrm{4.18} \text{Joules}$ is correct.

2. Checking the second relation: 1 Å = 10^-10 m
An Angstrom (Å) is a unit of length used chiefly in measuring wavelengths of light, atoms, and molecules. By definition:
$1 \text{Å}={\mathrm{10}}^{-10} \text{m}$
Thus, this relation is correct.

3. Checking the third relation: 1 MeV = 1.6 × 10^-13 Joules
An electron-volt (eV) is the amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. One eV is equal to:
$1 \text{eV}=\mathrm{1.6}\times {\mathrm{10}}^{-19} \text{Joules}$
A Mega-electron-volt (MeV) is equal to ${\mathrm{10}}^6 \text{eV}$. Therefore:
$1 \text{MeV}={\mathrm{10}}^6\times \left(\mathrm{1.6}\times {\mathrm{10}}^{-19} \text{J}\right)=\mathrm{1.6}\times {\mathrm{10}}^{-13} \text{Joules}$
Thus, this relation is correct.

4. Checking the fourth relation: 1 Newton = 10^-5 Dynes
Newton (N) is the SI unit of force, defined as:
$1 \text{N}=1 \text{kg}\cdot \text{m}/{\text{s}}^2$
Dyne (dyn) is the CGS unit of force, defined as:
$1 \text{dyne}=1 \text{g}\cdot \text{cm}/{\text{s}}^2$
Let us convert Newton into CGS units:
$1 \text{kg}={\mathrm{10}}^3 \text{g}$
$1 \text{m}={\mathrm{10}}^2 \text{cm}$
Substituting these values:
$1 \text{Newton}=\left({\mathrm{10}}^3 \text{g}\right)\times \left({\mathrm{10}}^2 \text{cm}\right)/{\text{s}}^2={\mathrm{10}}^5 \text{g}\cdot \text{cm}/{\text{s}}^2={\mathrm{10}}^5 \text{Dynes}$
Therefore, $1 \text{Newton}={\mathrm{10}}^5 \text{Dynes}$, making the statement $1 \text{Newton}={\mathrm{10}}^{-5} \text{Dynes}$ incorrect.

Hence, the wrong relation is 1 Newton = 10^-5 Dynes.