Explanation for the spectrum of the sun? 
My Question is, why exactely does the intensity vanish below 240 nm ?
If i look at the plank's law, obviously the intensity for $\lambda \rightarrow 0$ and $\lambda \rightarrow \infty$ will vanish, but why does it already vanish for $\lambda \approx 240 nm$ ?
sincerely
 A: It seems to me that the person drawing the graph was a bit sloppy - the ideal black body radiation ("idealer Schwarzer Körper" - Temperatur 5900 K) does not cut off sharply at 240 nm as shown. Instead, it should look like this:

when calculated from Planck's Law. I suspect some bug in the method used to calculate the values in the plot you reproduced - note that at the extremes of the plot, there is the possibility of overflow if the calculation is done carelessly (or in single precision). I suspect that is what happened here.
If you want to make this graph yourself, you could use (or adapt) this Python code snippet:
import math
from scipy.constants import codata
import numpy as np
import matplotlib.pyplot as plt

D = codata.physical_constants

h = D['Planck constant'][0]
k = D['Boltzmann constant'][0]
c = D['speed of light in vacuum'][0]

pi = math.pi

def planck(T, l):
    p = c*h/(k*l*T)
    if (p > 700):
        return 1e-99
    else:
        return (h*c*c)/(math.pow(l, 5.0) * (math.exp(c*h/(k*l*T))-1))        

Tvec=[5900]
Lvec = np.logspace(-8, -5.3, 1000)

plt.figure()
# create a semitransparent "rainbow plot" to show where visible range is:
plt.imshow(np.tile(np.linspace(0,1,100),(2,1)), extent=[400, 800, 0, 1], aspect='auto', cmap='rainbow', alpha = 0.4)

# compute Planck for a range of wavelengths
for T in Tvec:
    r = []
    for l in Lvec:
        r.append(planck(T, l))
    plt.plot(Lvec*1e9, r/np.max(r),label='T=%d'%T)
plt.xlabel('lambda (nm)')    
plt.title('wavelength distribution of black body (T=5900)')
plt.xlim((0,2500))
plt.show()

A: I don't think you can draw such conclusions from a simple graphic.  They've probably just cut it off at somewhere around 200nm because the power output at shorter wavelengths is almost irrelevant.
If you want a more accurate graph for shorter wavelengths, try this one.  You can set it up for 5900K and graph values below 240nm.
A: From the wiki article on the sun's radiation:


Solar irradiance spectrum above atmosphere and at surface. Extreme UV and X-rays are produced (at left of wavelength range shown) but comprise very small amounts of the Sun's total output power.

You ask:

My Question is, why exactly does the intensity vanish below 240 nm ? If i look at the plank's law, obviously the intensity for λ→0 and λ→∞ will vanish, but why does it already vanish for λ≈240nm ?

Of course the formula has values below but th statement  above is that there is very small radiation for λ≈240nm from the real sun spectrum. You will observe that the fit to the black body spectrum is approximate. The reason is that no real body has the assumptions that enter the derivation of the Planck formula, uniform quantum harmonic oscillators. 
Matter is composed of atoms and molecules and the sun particularly is in a very dense plasma state with magnetic fields ranging through . Therefore the fit to the black body is approximate. High energy photons have a small probability of being produced by thermal distributions and as far as measurements go they are not significant, due to the dynamics of the sun and the composition of its mass.
