The energy of emergent deuterons in a cyclotron can be determined using the formula:

E = qV

Where:
E is the energy of the emergent deuterons,
q is the charge of the deuterons, and
V is the voltage applied across the dees of the cyclotron.

To calculate the energy, we need to find the charge of the deuterons and the voltage applied.

Finding the charge of deuterons:
Deuterons are ions of heavy hydrogen, with a mass number of 2. Since they are ions, they have a charge. The charge of an ion is given by the formula:

q = n × e

Where:
q is the charge of the ion,
n is the number of elementary charges, and
e is the charge of an electron.

Since deuterons have a charge of +1, we can substitute n with 1:

q = 1 × e = 1.6 × 10^-19 C

Finding the voltage applied:
The voltage applied across the dees of the cyclotron can be calculated using the formula:

V = B × r × 2π × m / q

Where:
V is the voltage applied,
B is the magnetic field strength,
r is the radius of the dees,
m is the mass of the deuterons, and
q is the charge of the deuterons.

Given that the magnetic field strength is 0.7T and the radius of the dees is 1.8m, and the mass of deuterons is approximately 3.34 × 10^-27 kg, we can substitute these values into the formula:

V = (0.7T) × (1.8m) × (2π) × (3.34 × 10^-27 kg) / (1.6 × 10^-19 C)

Calculating this expression will give us the voltage applied.

Finally, we can substitute the charge of the deuterons and the voltage applied into the energy formula:

E = (1.6 × 10^-19 C) × (calculated voltage)

Calculating this expression will give us the energy of the emergent deuterons in the cyclotron.