Is there a psychometric tool for measuring the difficulty of mental activities? It is often stated that Alzheimer's disease can be prevented to some extent when a person engages more often in challenging mental activities (http://www.mayoclinic.org/diseases-conditions/alzheimers-disease/basics/risk-factors/con-20023871)

Although I can imagine that solving mathematical problems is more difficult than watching reality shows on TV, the criteria for this classification are vague to me (Ok not so vague because mathematics requires more cognitive load, but this may not be the only factor). I am interested in how could a psychometric scale that quantifies level of difficulty in a broad range of activities be constructed as it would be useful in research on prevention and rehabilitation of certain neurocognitive disorders. 

Has such a scale been developed?
There is a workload measure called the NASA-TLX (Task Load Index), one component of which measures mental workload.  It is self-reported workload, however, and also requires interrupting most tasks, so it has some theoretical as well as practical weaknesses.

There is also decently good data that working memory load can be extracted from theta-band activity in the frontal regions, possibly due to the parieto-frontal circuits between the anterior cingulate, inferior frontal, and posterior parietal cortices.

(All of this, however, assumes that working memory load and "difficulty" are the same thing.)

Nasa-Task Load Index (NASA-TLX); 20 Years Later. Hart, S. (2006). Proceedings of the Human Factors and Ergonomics Society Annual Meeting October 2006 vol. 50 no. 9 904-908 doi: 10.1177/154193120605000909

Evidence for effects of task difficulty but not learning on neurophysiological variables associated with effort. Brouwer, A. &amp; al. (2014). International Journal of Psychophysiology Volume 93, Issue 2, August 2014, Pages 242–252. 
doi: 10.1016/j.ijpsycho.2014.05.004

Working memory load modulation of parieto-frontal connections: Evidence from dynamic causal modeling. Ma, L.; Steinberg, J.; Hasan, K.; Narayana, P.; Kramer, L.; et al. Human Brain Mapping 33.8 (Aug 2012): 1850-1867.
doi: 10.1002/hbm.21329